Chapter 49: Further topics
491
Equidistributed sequences
The asymptotic density ideal Z; equidistributed sequences;
when equidistributed sequences exist;
Z=PN/Z; effectively regular measures;
equidistributed sequences and induced embeddings of measure algebras
in Z.
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; L0; isometry groups of
spheres in inner product spaces; locally compact groups.
494
Groups of measure-preserving automorphisms
Weak and uniform topologies on AutμA; 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([I]<ω); and
Τ-removable intersections; the Hypergraph Removal Lemma;
Szemerédi's theorem; a multiple recurrence theorem.
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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