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 *C*_{0}(*X*); Radon measures
on *C*(*X*); separately continuous functions; convex hulls.

463
**T**_{p} and **T**_{m}

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**(

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 *L*^{0} and
*L*^{1}; *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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Revised 5.4.2016