Chapter 33: Maharam's theorem
331
Maharam types and homogeneous measure algebras
Relatively atomless algebras; one-step extension of
measure-preserving homomorphisms; Maharam type of a measure algebra;
Maharam-type-homogeneous probability algebras of the same Maharam type are isomorphic;
the measure algebra of {0,1}κ is homogeneous.
332
Classification of localizable measure algebras
Any localizable measure algebra is isomorphic to a simple product of
homogeneous totally finite algebras; complete description of
isomorphism types; closed subalgebras.
333
Closed subalgebras
Relative Maharam types; extension of measure-preserving Boolean
homomorphisms; complete classification of closed subalgebras of
probability algebras as triples (A,μ,C);
fixed-point subalgebras.
334
Products
Maharam types of product measures; infinite powers of probability
spaces are Maharam-type-homogeneous.
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