Chapter 46: Pointwise compact sets of measurable functions
461
Barycenters and Choquet's theorem
Barycenters; elementary properties; sufficient conditions for
existence; closed convex hulls of compact sets; Krein's theorem;
existence and uniqueness of measures on sets of extreme points;
ergodic functions and extreme measures.
462
Pointwise compact sets of continuous functions
Angelic spaces; the topology of pointwise convergence on C(X);
weak convergence and weakly compact sets in C0(X); Radon measures
on C(X); separately continuous functions; convex hulls.
463
Tp and Tm
Pointwise convergence and convergence in measure on spaces of
measurable functions; compact and sequentially compact sets;
perfect measures and Fremlin's Alternative; separately continuous
functions.
464
Talagrand's measure
The usual measure on P(I); the intersection of a sequence of
non-measurable filters; Talagrand's measure; the L-space of
additive functionals on P(I); measurable and purely
non-measurable functionals.
465
Stable sets
Stable sets of functions; elementary properties; pointwise
compactness; pointwise convergence and convergence in measure; a
law of large numbers; stable sets and uniform convergence in the
strong law of large numbers; convex hulls; stable sets in L0 and
L1; *R-stable sets.
466
Measures on linear topological spaces
Quasi-Radon measures for weak and strong topologies; Kadec norms;
constructing weak-Borel measures; characteristic functions of
measures on locally convex spaces; universally measurable linear
operators; Gaussian measures on linear topological spaces.
*467
Locally uniformly rotund norms
Locally uniformly rotund norms; separable normed spaces; long
sequences of projections; K-countably determined spaces; weakly
compactly generated spaces; Banach lattices with order-continuous
norms; Eberlein compacta and Schachermeyer's theorem.
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