Contents of Measure Theory, by D.H.Fremlin

Chapter 33: Maharam's theorem

331 Classification of 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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Revised 2.10.08