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% % %I offer this version of the index in its TeXfile form, so that %(if you have a fast connection and can put up with the formatting) %you can check for individual terms with control-F %without leaving your browser. %
\frfilename{mt6i.tex} \versiondate{22.3.13/7.6.14} \copyrightdate{2013} \def\iiv{ii_{\pmb{v}}} \def\iivu{\iiv(\pmb{u})} %\def\indexheader#1{\ifnum\volumeno<6{}\else\indexheader{#1}\fi} \volumeno=6 \Centerline{\bf Index to Volume 6} In this index, I list definitions of terms used in Volume 6, but make no further attempt to cover the material in other volumes. Definitions marked with $\pmb{>}$ are those in which my usage is dangerously at variance with that of some other author or authors. \medskip \indexheader{absolutely} absolutely continuous real function 618D \indexheader{accessibility} accessibility {\it see} region of accessibility ({\bf 643C}) \indexheader{adapted} adapted local interval function {\bf 613C}, 613D, 613E, 613F, 613G, 613H, 613J, 613Xa, 613Yc, 619Xd, 636Yb, 633F, 639D; {\it see also} integrating interval function ({\bf 619B}) \indexheader{algebra} algebra {\it see} $f$-algebra ({\bf 352W}) \indexmedskip%B \indexheader{basic} basic stopping time {\it 617H proof} \indexheader{Bichteler} Bichteler-Dellacherie theorem 634K, 634L \indexheader{Borel} Borel measurable function 645Q, 645R \indexheader{bounded} bounded set {\it see} topologically bounded bounded stopping time {\bf 611Bb} bounded variation (real function) 614Xk, 615G, 618D, 645Xb ----- (process) 614K, {\bf 614L}, 614M, 631H, 631Ib, 614Xd, 614Xh, {\it 614Xi}, 614Xj, 614Xk, 614Xl, 614Xo, 615G, 619Hc, \S631, %631D, 631E, 631F, 631G, 631H, 631I, 631J, 631L, 631P, 631Xa 636Gb, 637Ld, 638Dd, 638Eb, {\it 638Yb}, 639Eb, 641Xc, 642Xb, 643H, 646Oc, 647Gd, 653Eb, 653G, 653H, 653L; {\it see also} locally bounded variation ({\bf 614Lb}), $\Mbv$ \indexheader{breakpoint} breakpoint string (for a simple process) {\bf 612H}, 612I, 612Xd \indexheader{Brownian} Brownian motion {\bf 612O}, 615Hb, 617J, 617O, 617Yc, 621Jc, 635T, 651F \indexmedskip%Ca \indexheader{\cadlag} \cadlag\ real function {\bf 4A2A}, 615D, 615G, 615Xb, 615Ya, 642E \cadlag\ process {\bf 615Xc}, 615Yd-615Yf; %615Yd, 615Ye, 615Yf {\it see also} $\Mcdlg$ ({\bf 615Xc}) \cadlag\ sample paths 615D, 642E \indexheader{capped} capped-stake variation set {\bf 614E} ----- ($Q_{\Cal S}(d\psi)$) {\bf 614Ea}, 619B ----- ($Q_{\Cal S}(d\pmb{u}\psi)$) 619Fa ----- ($Q_{\Cal S}(d\pmb{v})$) {\bf 614Ec}, 614Xc, 614Xk, 634J, 646N, 646Ya ----- ($Q_{\Cal S}(|d\pmb v|)$) {\bf 614Ec} ----- ($Q_{\Cal S}((d\pmb{v})^2)$) {\bf 614Ec} ----- ($Q_{\Cal S}(Pd\pmb{v})$) {\bf 633G}, 634Xb ----- ($Q_{\Cal S}(|Pd\pmb{v}|)$) {\bf 633G}, 634Xb ----- ($Q_{\Cal S}(d\pmb{v}d\pmb{w})$) {\bf 619Ia} ----- ($\widehat Q_{\Cal S}(d\pmb{v})$) {\bf 635Fb}, 635H %Q_{\Cal S}(d\psi) \indexheader{c\`agl\`ad} c\`agl\`ad function \indexheader{Cauchy} Cauchy distribution 617Ya Cauchy sequence 645F %Cb%Cc%Cd%Ce \indexheader{cell} cell (in `$I$-cell') {\bf 611Je}, 611K, 612Ib, 613Eb %Cf%Cg%Ch \indexheader{change} change of law 613Bg, 613I, 632B, 632C, 634K, 634Ld, 651I, 651J, 651Z change of variables 613Yc, 619G, 635N-635P, %635N, 635O, 635P 646P %Ci%Cj%Ck%Cl \indexheader{closed} closed subalgebra {\bf 323I}, 613Ab, \S638 %Cm%Cn%Co \indexheader{cofinal} cofinal subset of a partially ordered set {\bf 3A1Fa} \indexheader{coinitial} coinitial subset of a partially ordered set {\bf 511Bc} \indexheader{complete} complete linear topological space 613Bh, 635Dc, 635Xa complete measure space {\bf 211A}, 612F \indexheader{concave} concave function 634Ca \indexheader{conditional} conditional expectation {\bf 233D}, 616F, 643Bb ----- ----- operator {\bf 242Jf}, {\bf 365Ra}, 616Cb, 617B, 617E, 617Xe, 632B, 638Ga, 638H \indexheader{constant} constant process 612De constant stopping time {\bf 611Bb}, 611Ce, 611Ec, 611Ga, 612Fa, {\it 637D}, {\it 637J}, 636Xa, {\it 636Yc}, 639Cb \indexheader{continuous} continuous sample paths 642Gb continuous time 615Yc, 641L, 641H \indexheader{convergence} convergence in measure {\bf 245A}, {\bf 367L}, {\bf 613B}, 616Bc, {\it 613H}, {\it 613Xe}, 634G, 644Bc, 644C, 645Da, 645K \indexheader{convex} convex real function 618B convex set in a linear space 634F, 634G, {\it 634J} \indexheader{coordinated} coordinated (subalgebra coordinated with a filtration) {\bf 638Gb}, 638I-638L, %638I 638J 638K 638L {\it 638Qa}, 641Yb \indexheader{covariation} covariation {\bf 619H}, 619N, 619J, 619K, 622H, 631M, 635Pa, 635R, 638Qd, 641Xe, 651G-651I %651G, 651H, 651I \indexheader{cover} cover (in `$A$ covers $B$') {\bf 636B}, 636C-636G, %636C 636D 636E, 636F 636G, 637F, 636E, 636F; {\it see also} finitely cover ({\bf 636Ba}) \indexheader{covered} covered envelope {\bf 612Xe}, 612Xf, {\bf 636B}, 637G, 636Ya, 647J {\it see also} finitely-covered envelope ({\bf 636Bc}) \indexheader{covering} covering ideal {\bf 6F11M}, 612M, 612Xf, 614Xh, 613Yd, 614Xc, 615F, {\it 636Bb}, 646N, 646Ya %Cp%Cq%Cr%Cs%Ct%Cu \indexheader{cumulative} cumulative variation (of a process of bounded variation) {\bf 631Q}, 631E-631G, %631E, 631F, 631G, 631L, 653Eb, 653H, 653M %Cw%Cx%Cy%Cz \indexmedskip%D \indexheader{Dedekind} Dedekind complete lattice 611C, 612A, 645Ya \indexheader{Dellacherie} Dellacherie C.\ {\it see} Bichteler-Dellacherie theorem \indexheader{distribution} distribution (of a member of $L^0(\frak A)^n$) 616Xa \indexheader{distributive} distributive lattice 611C distributive law {\it 637Yc} \indexheader{dominated} dominated convergence theorem 645N \indexheader{Doob} Doob's maximal inequality 616E, 633Ba Doob's quadratic maximal inequality 653B Doob-Meyer theorem 633J-633L %633J, 633K, 633L \indexmedskip %E \indexheader{envelope} envelope {\it see} covered envelope, finitely-covered envelope {\bf 636Bb} \indexheader{exactly} exactly local interval function {\bf 636Yb} \indexheader{exponential} exponential process 651B-651I, %651B, 651C, 651D, 651E, 651F, 651G, 651H, 651I 651Xa \indexheader{extension} extension of fully adapted process 612Xd, 634H, 637M %F \indexheader{filtration} filtration (of closed subalgebras) {\bf 611Ba}, 612F, 617Xa, {\it 641Bc}, 638Ba, 638O, 638P, 647E %includes \frak A_t ----- (of $\sigma$-subalgebras) {\bf 615E} \indexheader{finite} finite-valued stopping time {\bf 611Bb} \indexheader{finitely} finitely cover (in `$A$ finitely covers $B$') {\bf 636B}, 647Hc finitely-covered envelope {\bf 636B}, 637E, 637H finitely full set {\bf 636Bc}, 637Ib, 636M, 636H, 636I, 636J, 636K, 639G, 643J, 643K \indexheader{free} free product (of probability algebras) {\it 638Q} \indexheader{full} full set of stopping times {\bf 612Xe}, 617Xg, {\bf 636Bc}; {\it see also} finitely full ({\bf 636Bc}) \indexheader{fully} fully adapted process {\bf 612D}, 612G-612I, %612G, 612E, 612Fb, 612H, {\it 612I}, 612L-612P, %612Lb, 612M, 612N, 612O, 612P, 612Xe, 612Xa, 612Xg, 613G, 613J, 613Xe, 614Xk, 617Xe, 621D, 621Xa, 622Fa, 634H, 636D, 636H, 637Be, 639D, 639Yb, 641Db, 642Bb, 643Eb, 643I, 643K, 646Ec, 646Ga, 647Gd, 647Ja; {\it see also} locally order-bounded process ({\bf 612N}), simple process ({\bf 612H}) \indexheader{fundamental} Fundamental Theorem of Martingales 643M \indexmedskip %G \indexheader{gauge} gauge integral 613H, 613Yb, 615Ya \indexheader{generate} generate {\it see} linearly generate ({\bf 611K}) \indexmedskip%H\indexmedskip%I \indexheader{ideal} ideal (in a lattice) {\bf 611Cf}, 612Xe, 617K, 617Xg, 617Yb; {\it see also} covering ideal ({\bf 611M}) \indexheader{identity} identity process {\bf 612Ec}, 614Xi, 614P, 615Ha, 615Ye, 617Xl, 619La, 619Xb, 621Ja, 631Xd, 635T \indexheader{independent} independent (stochastically independent) subalgebras 638N, 638P \indexheader{indefinite} indefinite (Riemann-sum) integral {\bf 613O}, 613Xd, 617M, 617N, 619Hb, 631I, 631J, 631Xb, 635I, 635I-635P, %635I 635J 635K 635L 635M 635N 635O 635P 635Xc, 641J, 646Kc, 651G, 651J, 651Xa, 653Ea, 653G, 653I indefinite S-integral 646J, 646L, 646M, 646P, 646R, 647Xa, 653K, 653M, 653O %\indexheader{inf-closed} %inf-closed set %\indexheader{integrable} \indexheader{integral} integral (Riemann-sum integral) (in $\int_{\Cal S}\pmb{u}\,d\psi)$) {\bf 613H}, 613I, 613J, 613Xm, 613Ya, 619E, 619F, 619G, 619M, 619Xd, 619Xf ----- (in $\int_{\Cal S}\pmb{u}\,d\pmb{v}$) {\bf 613K}, 613N, 613L, 613Xb, 613Xc, 613Yd, 619G, 619M, 619Xf, 631B, 631Db, 631J, 631Xd, 634J, 635Ed, 636F, 637H, 637I, 637Md, 638Dg, 638Ec, 639F, 639I, 641H, 641I, 641Xd, 644C, 644E, 644G-644L, %644G 644H 644I 644J 644K 644L 644Xb, 645G, 645J, 645K, 645Ma, 646Ef, 646P, 646Xd, 647Ge, 653Ea ----- (in $\int_{\Cal S}\pmb{u}\,d\pmb{v}d\pmb{w}$) {\bf 613Ka}, 613M, 637Q? ----- (in $\int_{\Cal S}\pmb{u}\,|d\pmb{v}|$) {\bf 613Ka}, 614K, 614Xl, 631B-631F, %631B, 631C, 631Db, 631E, 631F, 631I, 631J, 631L, 631P, 631Xa, 631Xd, 647Xa ----- (in $\int_{\tau}^{\tau'}\pmb{u}\,d\psi)$) {\bf 613H}, 613Ya, 639Db ----- (in $\int_{\tau}^{\tau'}\pmb{u}\,d\pmb{v}$) 613N, 613Xc, 613Yc, 614G, 615Yb, 615Yc, 617Xi, 619J, 637J, 637K, 635P; {\it see also} indefinite integral ({\bf 613O}) ----- (in $\int_{\tau}^{\tau'}\pmb{u}\,(d\pmb{v})^2$) {\bf 613Kb}, 613Xc, 619H ----- (in $\int_{\tau}^{\tau'}\pmb{u}\,|d\pmb{v}|$) {\bf 613Kb} %----- (in $\int_{\tau}^{\tau'}\pmb{u}\,Pd\pmb{v}$) %----- (in $\int_{\tau}^{\tau'}\pmb{u}\,|Pd\pmb{v}|$) ----- (in $\int_{\tau}^{\tau'}\pmb{u}\,d\pmb{v}d\pmb{w}$) 619H, 619J, 635N, 635O ----- {\it see also} S-integral ({\bf 645La}) integral equation {\it see} Picard's theorem \indexheader{integrating} integrating interval function {\bf 619B}, 619C-619G, %619C, 619E, 619F, 619G, 619M, 619I, 619Xa, 619Xd, 619Xf, 631Da, 635J \indexheader{integrator} integrator (stochastic process) {\bf 614F}, 614R, 614G, 614H, 614N, 614Xc, 614Xk, 614Yb, 617E, 617F, 617Xf, 618B-618D, %618B, 618C, 618D, 619B, 619G, 619M, 619I, 619J, 619Xf, 622G, 634Ib, 634K-634N, %634K, 634Ld, 634N 634Xd, 634Z, 635H, 635I, 635M-635P, %635M, 635N, 635O, 635P, 635R, 636G, 637J, 637L, 638De, 638Eb, 638Jb, {\it 638Yb}, 639Ec, 639F, 639H, 639I, 641J, 645B-645D, %645Bb, 645Cb, 645D, 645J, 645K, 645M, 645N, 645Xd, 646L, 647Gf; {\it see also} continuous integrator, local integrator ({\bf 614Fb}), quasi-integrator ({\bf 634Bd}), strong integrator ({\bf 634Bc}) \indexheader{interval} interval function {\it see} adapted local interval function ({\bf 613C}) \indexheader{invariance} invariance under change of law 613I, {\it 613 notes} \indexheader{It\^o} It\^o's formula 622B, 622C, 622H, 622Ya, 646Q \indexmedskip%J \indexheader{Jensen} Jensen's lemma 616Cd \indexheader{jump} jump-free process {\bf 621Bb}, 621E, 621I, 621Xc, 621Xd, 621Xe, 621Xf, 631G, 631Hb, 631O, 631P, 631Xc, 635Mb, 635Ra, 636Gh, 636M, 636Kb, 637Lh, 637Mc, 638Df, 638E, 639Ee, 641H, 641Kb, 641Xe, 643F, 643G, {\it 644C}, {\it 644E}, 645Ma, 646Ob, 646Q, 651Ba, 651J; {\it see also} locally jump-free ({\bf 621Bb}), $\Mjf(\Cal S)$ ({\bf 621Ea}) \indexmedskip%K %\indexheader{Kunita} %Kunita-Watanabe 635N\query %perhaps `K-W formula'? \indexmedskip%L \indexheader{lattice} lattice homomorphism 612F, 639Cb \indexheader{Lebesgue} Lebesgue probability algebra 617Xa Lebesgue-Stieltjes measure 615Ya, 615Yb, 645Xb indexheader{L\'evy} L\'evy process 612P, 617Xb, 617Ya, 638Q \indexheader{linear} linear space topology 644J, 644Xg; {\it see also} convergence in measure, ucp topology ({\bf 635Cb}) \indexheader{linearly} linearly generate (in `linearly generate $I$-cells') {\bf 611L}, 612Dd \indexheader{Lipschitz} Lipschitz function {\bf 262A}, 614M, 622G, 653H, 653I, 653M, 653O \indexheader{local} local integrator {\bf 614Fb}, 614H, 614I, 614Xc, 617G, 617Xm, 618B-618D, %618B, 618C, 618D 631M, 635Xc, 637K, 639J, 641K, 641Xe, 643M, 643Xc, 643Ya, 651B, 651G, 653I, 653O local interval function {\it see} adapted local interval function ({\bf 613Ca}), exactly local interval function ({\bf 636Yb}) local martingale {\bf 617Cc}, 617Hb, 617L, 617N, 617J, 617O, 617Xa, 617Xe, 617Xf, 617Xj, 617Xn, 617Yb, 619K, 633Xd, 633D, 632Bc, 634Ca, 635S, 638Q, 642Yb, 643Kb, 643L, 643M, 646L, 651C, 651H, 651I, 651J, 651Z; {\it see also} continuous local martingale, exponential local martingale local ucp topology {\bf 635Xa}, 635Xc \indexheader{locally} locally bounded variation (stochastic process) {\bf 614Lb}, 614Mb, 614Xf, 614Xi, 614N, 615G, 631M, 631Xb, 635S, 636Gb, 641Xf, 643L, 643M; {\it see also} $\Mlbv$ %normally "locally of bounded variation" locally jump-free process {\bf 621Bb}, 621F, 621J, 631M, 635Rb, 635S, 642Gb, 651B-651E, %651B, 651C, 651D, 651E, 651G, 651H, 653I, 653Xe, 653Xf locally near-simple process {\bf 614Bb}, 614C, 614I, 614P, 614Xe, 614Xj, 615B, 615D, 615F, 615H, 615Xb, 615Yd, {\it 615Yf}, 617Hc, 617L, 617N, 617Xb, 631M, 631Xb, 634Eb, 634N, 636Lb, 636Xe, 637N, 637I-637K, %637Ia, 637J, 637K, {\it 637Xa}, 638E, 638F, 639Ef, 639F, 639H-639J, %639H, 639I, 639J, 639Yb, 641D, 641Fa, 641G, 641K, 641Xc, 641Xe, 641Xf, 643B, 643Xc, 646Kc, 651B, 651G, 653Cb, 653I, 653O, 653Xf locally order-bounded process {\bf 612Kb}, 612L, 612Oc, 612Pf, 612Xf, 614J, 614N, {\it 617Ya}, 621D, 636Lb, 641Fa, 643Ic, 643K, 653Cb; {\it see also} $\Mlob$ ({\bf 635Xa}) locally S-integrable process {\bf 645Ld}, 646K, 653O locally solid topology {\bf 635Ya} \indexheader{lower} lower semi-continuous function 613Bc \indexmedskip %M \indexheader{martingale} martingale {\bf 616Da}, 616E, %6{}16E, 616G-616K, %616G 616H 616I 616J 616K 616Xa, {\bf 617C}, 617E, 617F, 617H-617M, %617H 617I 617J 617K 617L 617M {\it 617O}, 617Xa, 617Xc-617Xg, %617Xc 617Xe 617Xg 617Xi, 617Xm, 617Xn, {\it 617Yc}, 632Bd, 633B, 633D, 633J, 633K, 633Xb, 633Xc, 634Ca, 635Xb, 637Ja, 639Ed, 642Xb, 643Bb, 643H, 643Ib, 643L, 643Ya, 644I, 646N, 646L, 651D-651F, %651D 651E 651F 651J, 651Z, 653B, 653G, 653H, 653L ----- {\it see also} local martingale ({\bf 617Cc}), quasi-martingale ({\bf 634Bb}), semimartingale ({\bf 617Cd}), strong martingale ({\bf 634Bc}), submartingale ({\bf 633H}), supermartingale ({\bf 634Ba}) \indexheader{maximal} maximal inequality 616E \indexheader{measurable} measurable space with negligibles 622De \indexheader{measure-converging} measure-converging filter 637K \indexheader{measure-preserving} measure-preserving Boolean homomorphism 616F-616H %616F, 616G, 616H \indexheader{modular} modular function {\it 612Df}, {\it 612Xa} \indexheader{multiplicative} multiplicative Riesz homomorphism 612Ad, 641Fb, 642K \indexmedskip%N \indexheader{near} near-simple process {\bf 614B}, 614C, 614D, 614G, 614Xa, 614Xb, 614Xj-614Xn, %614Xj, 614Xk, 614Xm, 614Xn, 614Xp, 614Yc, 614Yd, 617Xa, 619I, 621Xb, 631F, 631H-631L, %631Ha 631I 631J 631L 631N-631P, %631N 631O 631P 631Xc, 635M-635P, %635Ma, 635N, 635O, 635P, 636G, 636Ka, 636Lb, {\it 636Yc}, 637Db, 637Ed, 637Xb, 638Ed, 639H, 639Yb, 641H, 641I, 641J, 641Kb, 641Xe, 645B, 645J, 645K, 645M, 645O, 646Ee, 646Gb, 646L, 646Xc, 647Gd, 653C, 653E, 653G, 653H, 653K-653M; %653K, 653L, 653M; {\it see also} locally near-simple ({\bf 614Bb}), $\Mns$ ({\bf 635Eb}) %O \indexheader{order} order-bounded process {\bf 612Ka}, 612Xe, 612Xg, 614Ba, 614Ma, 614Xk, 621B, 634D, 634Ia, 636Gb, 636Lb, 636I, 637G-637I, %637G, 637H, 637Ia, 637Lc, 638Dc, 638E, 639Ea, {\it 639F}, 641G, 643Ic, 645Z, 646Ed, 646Ga, 647Gd, 647Jb, 653Cb, 653Ec; {\it see also} locally order-bounded ({\bf 612Kb}), previsibly order-bounded ({\bf 645Ba}), uniformly order-bounded ({\bf 644Ba}), $\Mob$ ({\bf 612La}) order-bounded set 645F, 645G order-closed on the right {\bf 615Xc} order-closed set 636Ya order-closed subalgebra 611Ba, 611D, 612A, {\it 613Ab} order-closed Riesz subspace 612Ga order-continuous function 611Ci, 612Yb order-convex set {\bf 4A2A}, 614Yd, 615B, 615F, 615Xa, 636Cb, 637D, 637E, 637N, 637Ia, 637J, 637L, 638E, 638F, 645J-645O, %645J, 645K, 645L, 645M, 645N, 645O, 645Xa, 645Xd order-convex hull {\it 637Xb}, 638F order topology {\it 612Ya}, {\it 637D}, {\it 637J}, 643N, 643Xd order*-convergent sequence (in $L^0$) 642B, 642Xd, 645N order*-convergent sequence (of processes) {\bf 642B}, 642Kc, 642Xb, 642Xc, 644C, 644E, 644G, 644H, 644L, 644Xa \indexheader{oscillation} oscillation (in $\Osclln_J(\pmb{u})$) {\bf 621B}, 636E, 636M ----- (in $\Osclln^*_I(\pmb{u})$) {\bf 621B}, 621C ----- (in $\Osclln(\pmb{u})$) {\bf 621B}, 621D, 621Xb, 621Xe, 621Xf, 635Ec, 641G, 643H, 643Ic, 643K-643M %643Kd, 643L, 643M % \Osclln \Osclln^* \indexmedskip %P \indexheader{partially} partially ordered linear space 645Ya \indexheader{partition} partition of unity 611G, {\it 611I} \indexheader{partially} partially ordered set 611B \indexheader{Picard} Picard's theorem 653H, 653I, 653O \indexheader{pointwise} pointwise convergence of a sequence of functions 642B, 642Kc \indexheader{Poisson} Poisson process {\bf 612P}, 614Xi, 614Xe, 615Hc, 617P, 617Xl, 619Lb, 619Xc, 621Jb, 633O, 638Q, 641Xb, 642Yb, 643Xb \indexheader{Polish} Polish topological space 611Ya \indexheader{pre-order} pre-order {\bf 645Ya} \indexheader{previsible} previsible process {\bf 642C}, 642D, 642K, 642Xd, 642Xe, {\it 642Ya}, {\it 642Yb}, 645O {\it see also} $\Mpv$ previsible variation {\bf 633M}, {\bf 633L}, 633Xa, 633Xe, 633Xf, 635V, 638Qd, 642Ya, 643F, 643G previsible version of a process 641Db, {\bf 641E}, 641F, 641G, 641H, 641I, 641J, 641Ka, 641Xb-641Xf, %641Xb 641Xc 641Xd 641Xe 641Xf 642Db, 642Eb, 642Fb, 642Xd, 643Xe, 644C, 644E, 644G, 644H, 644L, 645B-645D, %645B, 645Ca, 645Db, 645H, 645J, 645K, 645Ma, 645N, 645Xd, 646Ed, 646Gb, 646J, 646Kc, 646R, 647B, 647Gg, 653Kb, 653M, 653N, 653O previsible $\sigma$-algebra {\bf 642H}, 642I \indexheader{previsibly} previsibly order-bounded process {\bf 645Ba}, 646Gc; {\it see also} uniformly previsibly order-bounded ({\bf 645Ba}), $\Mob^0$ ({\bf 645Ba}) previsibly simple process {\bf 615Yc} \indexheader{probability} probability algebra 613A probability space 612F \indexheader{process} process {\it see} fully adapted process ({\bf 612D}) \indexheader{product} product $f$-algebra 612B product measure 638M \indexheader{progressively} progressively measurable stochastic process {\bf 455Le}, 612Fb, 612Xb, 615D, 637Xa \indexmedskip%Q \indexheader{quadratic} quadratic variation {\bf 619H}, 619N, 619K, 619L, 619Xb, 619Xc, 619Xe, 622B, 622C, 622Ya, 631L, 631M, 633Xb, 633Xc, 633Xd, 635P-635T, % 635P, 635R, 635S, 635T 635V, 636Gi, 637Li, 639J, 641K, 644I, 646Q, 651B, 651E, 651J, 653G, 653H, 653L, 653M \indexheader{quasi-integrator} quasi-integrator {\bf 634Bb}, 634I \indexheader{quasi-martingale} quasi-martingale {\bf 634Bb}, 634E, 634K, 634Lc, 634Xa-634Xc, %634Xa, 634Xb, 634Xc 634Xe \indexmedskip%R \indexheader{region} region of accessibility {\bf 643C}, 643Db, 643E, 643G, 643Xa, 643Xb, 643Xe, 645Xd \indexheader{relatively} relatively (stochastically) independent subalgebras {\bf 638Ga}, 638H, 638I, 638O \indexheader{representation} representation of stopping time {\bf 612Fa} \indexheader{residual} residual oscillation {\bf 621B}, 621D, 641G, 642Ga, 621Xa, 621Xd, 631G, 631N, 631Xc, 641G, 641Kb, 641Xe, 642Ga, 653E \indexheader{Riemann} Riemann sum 613E Riemann-sum integral {\it see} integral ({\bf 613H}) \indexheader{Riesz} Riesz homomorphism 612Ga, 612Yd Riesz space 612Ga, 645Ya \indexheader{right-continuous} right-continuous family of stopping times {\bf 639B}, 639Cd right-continuous filtration (of closed subalgebras) {\bf 611Ba}, 611C, 611Ed, 611Ge, 611Xa, 612Ob, 612Pc, 612Yb, 615B, {\it 615D}, 615F, 615Yd-615Yf, %615Yd, 615Ye, 615Yf 617Ec, 617Hc, 617L, 617N, 617O, 617Xa, 619K, 621I, 621Xd, 633Xd, 633E, 633J, 633K, 633L, 633Xa, 633Xc, 632C, 634Eb, 634N, 635S, 635U, 635V, 636Yc, 637N, 637I, 637J, 637L, 637Xb, 638B, 638E, 638F, 638Oc, 638P, 638Qa, 638Yb, \S639, 641H, {\it 642G}, 643D, 643E, 643G, 643H, 643L, 643M, 643Xc, 643Ya, 644D, 644E, 644G-644J, %644G 644H 644I 644J 644L, 645J-645O, %645J, 645K, 645L, 645M, 645N, 645O, 645R, 645Xa, 645Xd, 646C, 646D, 646I-646Q, %646I, 646N, 646J, 646L, 646P, 646Q, 646M, 646Xc, 646Xd, 646Ya, 647H-647K, %647H, 647I, 647J, 647K, 647Xa, 651C-651E, %651C, 651D, 651E, 651H-651J %651H, 651I, 651J, 653G-653I, %653G, 653H, 653I, 653K-653O %653K, 653L, 653M, 653N, 653O ----- (of $\sigma$-subalgebras) {\bf 615E} \indexmedskip %S \indexheader{semimartingale} semimartingale {\bf 617Cd}, 617G, 617Xb, 617Xh, 617Xm, 617Xn, 632C, 634N, 634Z, 643M, 643Xc, 646Ya, 651Z \indexheader{seminorm} seminorm {\it see} F-seminorm \indexheader{separating} separating sublattice {\bf 637B}, 637C, 637D, 637E, 637N, 637Ia, 637L, 637Xa, 639F, 639I, 639J \indexheader{sequentially} sequentially order-continuous function 621Ad, 622Da \indexheader{simple} simple process {\bf $\pmb{>}$612H}, 612I, 612J, 612Xc, 612Xd, 612Xf, 612Xg, 612Xh, 612Xi, 613N, 614Xo, 615Xd, 615Yd, 631N-631P, %631N 631O 631P 631Xa, 631Xc, 631Xd, 634J, 635K, 635L, 637Da, 637Ed, 637L, 639Yb, 641Db, 642Fa, 641I, 641Xd, 645Yb, 647Gd, 653Ca; {\it see also} near-simple ({\bf 614Ba}), previsibly simple ({\bf 615Yc}), $\Msimp$ ({\bf 635Ea}) simple stopping time {\it 617H proof}, 636Xa, 636Yc \indexheader{solid} solid hull {\bf 613Bf}, 616Be solid linear subspace 612Nc solid set 635Ya \indexheader{solid} split interval {\it 639Yb} \indexheader{square} square-integrable process 617M \indexheader{standard} standard Poisson process {\it see} Poisson process ({\bf 612P}) \indexheader{starting} starting value (of a simple process) {\bf 613N} \indexheader{Stieltjes} Stieltjes integral 613S \indexheader{stochastic} stochastic process {\it see} fully adapted process ({\bf 612D}) \indexheader{Stone} Stone space of a Boolean algebra 611Xc \indexheader{stopped} stopped process 612Gb, 613Yc \indexheader{stopping} stopping lemma 615B, 621I stopping time {\bf 611Bb}, 611I, 612F, 611Xc, 637Bb, 637K; {\it see also} $\Cal T$ stopping-time interval {\bf 611J}, 611K, 611Xc \indexheader{strong} strong integrator {\bf 634Bc}, 634Cb, 634L, 634Xe \indexheader{sublattice} sublattice 611Ca, 611K, 612Xe \indexheader{submartingale} submartingale {\bf 616Db}, %6{}16Eb, 616L, {\bf 633H}, 633I, 633J, 633K, 633L, 633Xa, 633Xe, 633Xf, {\it 634Ba}, 634La, 634Xc, 635V, {\it 642Ya}, 643F, 643G \indexheader{supermartingale} supermartingale {\bf 634Ba}, 634C-634E, %634Ca, 634D, 634E, 634Lb, 634Xe \indexmedskip%T \indexheader{tagged} tagged partition structure allowing subdivisions 613Yb \indexheader{topologically} topologically bounded set (in a linear topological space) {\bf 3A5N}, {\bf 613Bf}, 614F, 619B, 634G, 635H, 645Ga \indexheader{totally ordered set} 611B \indexmedskip%U \indexheader{uniformly} uniformly continuous function 645Da, 645P, 646M uniformly integrable process {\bf 617Ce}, 617De, 617Ea, 617Xm, 633D, 634Eb, 634K, 642Xb, 651D ----- ----- set (in $L^1(\frak A,\bar\mu)$) {\bf 616B}, 633Db, 646N, 646Ya uniformly order-bounded family of processes {\bf 644Ba}, 644C, 644E, 644G, 644H, 644J-644L %644J, 644K, 644L, 645Ba, 645H, 645K, 645Xa uniformly previsibly order-bounded family of processes {\bf 645Ba}, 645P, 645N, 646M \indexheader{upper} upper envelope (in a Boolean algebra) {\bf 313S} %\upr ----- ----- (of a stopping time) {\bf 637Ka}, 637L upper integral 645Xb \indexmedskip%V \indexheader{variation} variation of a process {\it see} bounded variation ({\bf 614La}), cumulative variation ({\bf 631Q}), locally bounded variation ({\bf 614Lb}), previsible variation ({\bf 633L}), quadratic variation ({\bf 619H}) \indexmedskip%W \indexheader{weak} weak topology 633L weak* topology 634F \indexheader{weakly} \wsid\ Boolean algebra 611Mf, 611Yd, 643D \indexheader{well} well-ordered set 612Ec Wiener measure {\bf 477D}, 612Oa, 617O \indexmedskip%X\indexmedskip%Y\indexmedskip%Z\indexmedskip \indexheader{$\scriptstyle\pmb{A}$} $\frak A_t$ {\it see} filtration $\frak A_{\tau}$ {\bf 611D}, 611E, 611Ga, 611H, 611I, 611Xb, 612D, 641Ba, 641Cb, 638I, 641B, 641Cb, 647Gb $\frak A_{\tau^-}$ {\bf 641B}, 641Ca, 641Da, 642Ea, 641Xa, 641Ya, 641Yb, 643Bb, 643C, 646B %\indexmedskip\indexheader{$\scriptstyle\pmb{B}$} \indexmedskip\indexheader{$\scriptstyle\pmb{C}$} \indexheader{ccc} ccc Boolean algebra 611Xd %\indexmedskip\indexheader{$\scriptstyle\pmb{D}$} \indexmedskip\indexheader{$\scriptstyle\pmb{E}$} $E$ (in $E_I$) {\it see} cell ({\bf 611Je}) $\Expn$ {\bf 613Aa}, 632B \indexmedskip\indexheader{$\scriptstyle\pmb{F}$} $f$-algebra {\bf 352W}, 612Ad, 612B, 612Nc, 635E, 635Xa, 642Bb, 645Ca, 645I $f$-algebra homomorphism {\bf 612Ad}, 636Da, 646Ga F-seminorm 635B, 636J, 645C $f$-subalgebra {\bf 612Ad}, 612Bc, 612Ga, 612Yd, 614M, 615Xc, 618C, 642Da %\indexmedskip\indexheader{$\scriptstyle\pmb{G}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{H}$} \indexmedskip\indexheader{$\scriptstyle\pmb{I}$} $\Cal I$ (in $\Cal I(\Cal S)$) {\bf 613Ha} $ii$ (in $\iivu$) {\it see} indefinite integral ({\bf 613O}) \indexmedskip\indexheader{$\scriptstyle\pmb{J}$} $\Mjf$ (in $\Mjf(\Cal S)$) {\bf 621E}, 635Ec, 635Mb %jump-free %\indexmedskip\indexheader{$\scriptstyle\pmb{K}$} \indexmedskip\indexheader{$\scriptstyle\pmb{L}$} $L^0$ (in $L^0(\frak A)$) 611Ba, 611Ga, 612A, 612Ga, 613Aa, 642B $L^1(\frak A,\bar\mu)=L^1_{\bar\mu}$ 632B, 634G $L^1$-process {\bf 617Ca}, 617Xn, {\it 633H}, 634B, 634Xb, 635U, 646Ya $L^2$-martingale 633Xc, 635V, 644I $L^p$-process {\bf 617Ca}, 617Xj, 633Xd $L^{\infty}$ (in $L^{\infty}(\frak A)$) 611Xa $L^{\infty}$-process {\bf 617Ca} $\liminf$ {\it 635U} \indexmedskip\indexheader{$\scriptstyle\pmb{M}$} $M$ (in $M(\Cal S)$, the space of fully adapted processes) 612G, 613Bl $\Mbv$ (in $\Mbv(\Cal S)$) {\bf 614M}, 631C, 645Ya $\Mcdlg$ (in $\Mcdlg(\Cal S)$) {\bf 615Xc} $\med$ (in $\med(p,q,r)$, where $p$, $q$, $r$ belong to a distributive lattice) {\bf 3A1Ic} $\Mlbv$ (in $\Mlbv(\Cal S)$, the space of processes locally of bounded variation) {\bf 614Mb} $\Mlob$ (in $\Mlob(\Cal S)$, the space of locally order-bounded processes) {\bf 612Lb}, 614Cd, {\bf 635Xa}, 635Xc $\Mns$ (in $\Mns(\Cal S)$, the space of near-simple processes) {\bf 635Eb}, 635I-635K, %635I, 635J, 635K, 635M, 641Fb, 644J, 645Db, 645Eb, 645G, 645K, 645Xa $\Mob$ (in $\Mob(\Cal S)$, the space of order-bounded processes) {\bf 612Lc}, 614Cd, 635C-635E, %635C, 635D, 635E, 635I-635K, %635I, 635J, 635K, 635Xb, 635Ya, 636J, 641Fb, 642Db, 653D $\Mob^0$ (in $\Mob^0(\Cal S)$, the space of previsibly order-bounded processes) {\bf 645Ba}, 645C-645F, %645C, 645D, 645E, 645F, 645H, 645I, 645K, 645Xb, 645Z $\Mpv$ (in $\Mpv(\Cal S)$, the space of previsible processes) 642D, 642Xa $\MSi$ (in $\MSi(\Cal S)$ {\bf 645Ec}, 645Ib, 653J; {\it see also} S-integrable ({\bf 645Lb}) $\MSi^0$ (in $\MSi^0(\Cal S)$) {\bf 645Eb}, 646Gd, 646M; {\it see also} S-integrable process ({\bf 645Lb}) $\Msimp$ (in $\Msimp(\Cal S)$, the space of simple processes) 613Xe, {\bf 635E}, 635Xa, 645Xe $M_{\text{sbm}}^+$ 633Xa $\med$ {\bf 3A1Ic} %\indexmedskip\indexheader{$\scriptstyle\pmb{N}$} \indexmedskip\indexheader{$\scriptstyle\pmb{O}$} $\Osclln$ (in $\Osclln_I(\pmb{v})$, $\Osclln^*_I(\pmb{v})$) {\it see} oscillation ({\bf 621Ba}) \indexmedskip\indexheader{$\scriptstyle\pmb{P}$} $P$ (in a conditional expectation $P_{\tau}$) {\bf 617A} $\pmb{P}$ (in $\pmb{P}u$, where $u\in L^1$) {\bf 617E}, 633L, 632B $Pd$ (in $Pd\pmb{v}$, where $\pmb{v}$ is an $L^1$-process) {\bf 633G}, 633L $P\Delta$ (in $P\Delta\pmb{v}$, where $\pmb{v}$ is an $L^1$-process) 636Yb, {\bf 633F}, 633G \indexmedskip\indexheader{$\scriptstyle\pmb{Q}$} $Q$ (in $Q_{\Cal S}$, $\widehat{Q}_{\Cal S}$) {\it see} capped-stake variation set ({\bf 614E}) %\indexmedskip\indexheader{$\scriptstyle\pmb{R}$} \indexmedskip\indexheader{$\scriptstyle\pmb{S}$} $S$ (in $S_I(\pmb{u},\psi)$) {\bf 613Eb}, 613G, 613H, 613Xb, 613Yc ----- (in $S_I(\pmb{u},d\pmb{v})$) 613Ed, {\bf 613Fb}, 613M, 614Ea, 631Bb, 636E, 637G ----- (in $S_I(\pmb{u},(d\pmb{v})^2)$) {\bf 613Fb}, 613M ----- (in $S_I(\pmb{u},|d\pmb{v}|)$) {\bf 613Fb}, 631E ----- (in $S_I(\pmb{u},Pd\pmb{v})$) {\bf 633G} ----- (in $S_I(\pmb{u},|Pd\pmb{v}|)$) {\bf 633G}, 634Xb $\widehat S$ (in $\widehat{S}_I(\pmb{u},d\pmb{v})$) {\bf 635F}, 635G S-integrable process 645Eb, 645H, 645I, 645K, {\bf 645Lb}, 645M-645O, %645M, 645N, 645O, 645R, 645Xb-645Xd, %645Xb, 645Xd 645Xe, 646B, 646C, 646I, 646J-646Q, %646J, 646L, 646P, 646Q, 646Xd, 653K, 653M, 653N S-integral ($\Sint$) {\bf 645La}, 645M, 645P, 645N, 645Xb, 646C, 646D, 646I, 647Jd, 647K; {\it see also} indefinite S-integral S-integration topology 645D, {\bf 645E}, 645F, 645H, 645K, 645P, 645N, 645Xb, 645Xe, 646J, 646M, 647C, 647Jc $\Sti$ (in $\Sti(\Cal S)$) {\it see} stopping-time interval ({\bf 611J}) $\Sti_0$ (in $\Sti_0(I)$) {\it see} cell ({\bf 611Je}) $\sup$ (in $\sup|\pmb{u}|$) {\bf 612Ka} \indexmedskip\indexheader{$\scriptstyle\pmb{T}$} $\Cal T$ (lattice of stopping times) 611B, 611C, \S638 $\Cal T_b$ (set of bounded stopping times) 611Bb, 611Cf, 611Me, 611Xa, 614Xk, 638Bb $\Cal T_f$ (set of finite stopping times) 611Bb, 611Cf, 611Me, 611Xa, 614Xk, 615D, 638Bb $\TSi$ {\it see} S-integration topology ({\bf 645E}) \indexmedskip\indexheader{$\scriptstyle\pmb{U}$} $u_{\tau^-}$ {\bf 641Db}, 641G, 642Eb, 643B ucp topology {\bf$\pmb{>}$ 635C}, 635D, 635E, 635Xb, 635Xe, 635Xf, 635Ya, 641Fb, 642Db, 644Xe, 645Db, 646M, 653D; {\it see also} local ucp topology ({\bf 635Xa}) $\upr$ (in $\upr(a,\frak B)$) {\it see} upper envelope ({\bf 313S}) %\indexmedskip\indexheader{$\scriptstyle\pmb{V}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{W}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{X}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{Y}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{Z}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\alpha}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\beta}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\gamma}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\Gamma}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\damma}$} \indexmedskip\indexheader{$\scriptstyle\pmb{\Delta}$} \indexheader{$\Delta$} $\Delta$ (in $\Delta\pmb{v}$) {\bf 613Cb}, 613Yc, 619B, 619I ----- (in $|\Delta\pmb v|$ 631Da ----- (in $\pmb{u}\Delta\pmb{v}$) 636Yb ----- (in $P\Delta\pmb{v}$) 636Yb ----- (in $\Delta_e(\pmb{u},\psi)$) {\bf 613Ea} ----- (in $\Delta_e(\pmb{u},d\pmb{v})$, $\Delta_e(\pmb{u},d\pmb{v}d\pmb{w})$, $\Delta_e(\pmb{u},|d\pmb{v}|)$) {\bf 613Fa}, 631Bb, 635L %\indexmedskip%epsilon\indexheader{$\scriptstyle\pmb{\epsilon}$} %\indexmedskip%zeta\indexheader{$\scriptstyle\pmb{\zeta}$} %\indexmedskip%eta\indexheader{$\scriptstyle\pmb{\eta}$} \indexmedskip\indexheader{$\scriptstyle\pmb{\theta}$} \indexmedskip\indexheader{$\theta$} $\theta$ (in $\theta(w)$, where $w\in L^0$) {\bf 613B}, {\it 613H}, 616J, 636H, 645Bb, 645J $\widehat{\theta}$ (in $\widehat{\theta}_A(\pmb{u})$) {\bf 635B}, 635C, 635Xa, 636H $\widehat{\theta}'$ (in $\widehat{\theta}'_A(\pmb{u})$) {\bf 636J}, 636Yd $\widehat{\theta}^{\#}$ (in $\widehat{\theta}^{\#}_{\pmb{v}}(\pmb{w})$ {\bf 645Bb}, 645Cb, 645D, 645J, 645Yb, 646Gc %\indexmedskip\indexheader{$\scriptstyle\pmb{\Theta}$}} %iota \indexmedskip\indexheader{$\scriptstyle\pmb{\iota}$} $\pmb{\iota}$ {\it see} identity process ({\bf 612Fc}) %kappa\indexheader{$\scriptstyle\pmb{\kappa}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\lambda}$} $\Lambdapv$ {\it see} previsible $\sigma$-algebra ({\bf 642H}) %\indexmedskip\indexheader{$\scriptstyle\pmb{\Lambda}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\mu}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\nu}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\omicron}$} \indexmedskip\indexheader{$\scriptstyle\pmb{\pi}$} $\bar\pi$ (in $\bar\pi_{\sigma}$) {\bf 639B} %\indexmedskip\indexheader{$\scriptstyle\pmb{\Pi}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\rho}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\sigma}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\Sigma}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\tau}$}} %\indexmedskip\indexheader{$\scriptstyle\pmb{\upsilon}$} %\indexmedskip\indexvheader{$\scriptstyle\pmb{\Upsilon}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\phi}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\Phi}$} \indexmedskip\indexheader{$\scriptstyle\pmb{\chi}$} $\chi$ (in $\chi a$, where $a$ belongs to a Boolean algebra) {\bf 361D} %\indexmedskip\indexheader{$\scriptstyle\pmb{\Chi}$} %\indexmedskip\indexheader{$\scriptstyle\pmb{\psi}$}} %\indexmedskip\indexheader{$\scriptstyle\pmb{\Psi}$}} \indexmedskip\indexheader{$\scriptstyle\pmb{\omega}$} $\omega_1$ (the first uncountable ordinal) 642Ya %\indexmedskip\indexheader{$\scriptstyle\pmb{\Omega}$} \indexmedskip\indexheader{1} 1 (the greatest element of a Boolean algebra) {\bf 311Ab} $\tbf 1$, $\tbf 1^{(\Cal S)}$ (constant processes with value $\chi 1$) {\bf 612De}, {\bf 641F} ----- processes $z\pmb u=z\tbf 1\times\pmb u$ {\bf 612De}, 612Jc, 612Lc, 612Xg, 613Kb, 613Xb, 614Ce, 614Hd, 614Xl, 615Xc, 617Xn, 619Xd, 619Xe, 621Xf, 633Xf, 635Xf, 641F, 642Xe, 645Da, 645Xd, 646D \indexmedskip\indexheader{special symbols} $\bar{\phantom{g}}$ (in $\bar h(u)$) {\bf 364H}, 612A, 612Ga, 612Nc, 613Bb, 615Xc, 642B ----- (in $\bar h(\pmb{u})$) {\bf 612B}, 612J, 612Yd, 614Cc, 614M, 618B-618D, %618B, 618C 618D 621Eb, 641Fa, 622B, 622C, 634Ca, 635Da, 635E, 636Da, 639I, 641Fa, 642Da, 645Ca, 645I, 646Xa, 646Xb ----- (in $\bar h(v_1,\ldots,v_k)$) {\bf 622D}, 622E, 622Xa, 622Xb ----- (in $\bar h(\pmb{v}_1,\ldots,\pmb{v}_k)$) {\bf 622E}, 622F-622H %622F, 622G, 622H, 653D, 653H, 653I, 653J, 653N, 653O $_-$ (in $\pmb{u}_-$) {\it see} previsible version {\bf 641E} $\|\,\|_1$ (in $L^1(\frak A,\bar\mu)$) 613B, 616E, 616H, 616J, 616K, 634Xb, 635U $\|\,\|_2$ (in $L^2(\frak A,\bar\mu)$) 616I, 616K, 653B, 653G, 653L $\|\,\|_p$ (in $L^p(\frak A,\bar\mu)$) 613Bc, 616Bd $\|\,\,\|_{\infty}$ (in $\|\pmb{u}\|_{\infty}$, where $\pmb{u}$ is a process) {\bf 612Na}, 612Xe $\Bvalue{\,\,}$ (in $\Bvalue{u>\alpha}$) {\bf 364A}, 612A ----- (in $\Bvalue{u\in E}$ {\bf 364G}, 612A ----- (in $\Bvalue{\sigma<\tau}$, $\Bvalue{\sigma\le\tau}$, $\Bvalue{\sigma=\tau}$) {\bf 611F}, 611G, 611J, 612Fa, 611Xc, 638Bd, 638Kc, 639Cc ----- (in $\Bvalue{\pmb{u}\ne\pmb{v}}$) {\bf 612Nb}, 612Xe, 636Da, 641Fa, 647K ----- (in $\Bvalue{(u_1,\ldots,u_k)\in E}$) {\bf 622D}, 622Xa $\covar{\phantom{i}}{\phantom{i}}$ {\it see} covariation ({\bf 619H}) $^*$ (in $\pmb{v}^*$, where $\pmb{v}$ is a process) {\it see} quadratic variation ({\bf 619H}) $\int$ (in $\int_{\Cal S}\pmb{u}\,d\psi$, etc.) {\it see} integral ({\bf 613H}, {\bf 613K}) $\Sint$ (in $\Sint_{\Cal S}\pmb{w}\,d\pmb{v}$) {\it see} S-integral {\bf 645La} $\preccurlyeq$ (in $\pmb{v}\preccurlyeq\pmb{v}'$) {\bf 645Bc}, 646F, 647I \discrpage