Chapter 49: Further topics

491
Equidistributed sequences

The asymptotic density ideal ** Z**; equidistributed sequences;
when equidistributed sequences exist;

492
Combinatorial concentration of measure

The Hamming metric; concentration of measure in product spaces;
concentration of measure in permutation groups.

493
Extremely amenable groups

Extremely amenable groups; concentrating additive functionals;
measure algebras under Δ; *L*^{0}; isometry groups of
spheres in inner product spaces; locally compact groups.

494
Groups of measure-preserving automorphisms

Weak and uniform topologies on Aut_{μ}**A**; a weakly mixing automorphism
which is not mixing; full subgroups and fixed-point subalgebras;
extreme amenability; automatic continuity; algebraic cofinality.

495
Poisson point processes

Poisson distributions; Poisson point processes; disintegrations;
transforming disjointness into stochastic independence; representing
Poisson point processes by Radon measures; exponential distributions
and Poisson point processes on [0,∞[.

496
Maharam submeasures

Submeasures; totally finite Radon submeasures; Souslin's operation;
(K-)analytic spaces; product submeasures.

497
Tao's proof of Szemerédi's theorem

Τ-removable intersections; and relative independence;
permutation-invariant measures on ** P**([

498
Cubes in product spaces

Subsets of measure algebras with non-zero infima; product sets
included in given sets of positive measure.

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Revised 1.6.2016