Chapter 46: Pointwise compact sets of measurable functions
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.
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.
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.
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.
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.
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.
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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