Contents of Measure Theory, by D.H.Fremlin

Chapter 52: Cardinal functions of measure theory

521 Basic theory
addμ and addN(μ); measure algebras and function spaces; the topological density of a measure algebra; shrinking numbers; π(μ); subspace measures, direct sums, image measures, products; perfect measures, compact measures; complete locally determined measure spaces and strict localizability; magnitudes; bounds on the Maharam type of a measure; countably separated spaces; measurable additive functionals on P(I).

522 Cichon's diagram
The cardinals b and d; inequalities linking them with the additivity, cofinality, uniformity and covering numbers of measure and category in the real line; the localization relation; mcountable and other Martin numbers; FN(PN); cofinalities of the cardinals.

523 The measure of {0,1}I
The additivity, covering number, uniformity, shrinking number and cofinality of the usual measure on {0,1}I; Kraszewski's theorems; what happens with GCH.

524 Radon measures
The additivity, covering number, uniformity and cofinality of a Radon measure; l1(κ) and localization; cardinal functions of measurable algebras; countably compact and quasi-Radon measures.

525 Precalibers of measure algebras
Precalibers of measurable algebras; measure-precalibers of probability algebras; (quasi-)Radon measure spaces; under GCH; precaliber triples (κ,κ,k).

526 Asymptotic density zero
Z is metrizably compactly based; NNTZTl1GTNNZ; cardinal functions of Z; meager sets and nowhere dense sets; sets with negligible closures; not-Nwd≤TZ and not-ZTNwd.

527 Skew products of ideals
NBN and Fubini's theorem; MBM and the Kuratowski-Ulam theorem; MBN; NBM; harmless Boolean algebras.

528 Amoeba algebras
Amoeba algebras; variable-measure amoeba algebras; isomorphic amoeba algebras; regular embeddings of amoeba algebras; localization posets; Martin numbers and other cardinal functions; algebras with countable Maharam type.

529 Further partially ordered sets of analysis
Lp and L0; L-spaces; the localization poset and the regular open algebra of {0,1}c; the Novák numbers n({0,1}I); the reaping numbers r1,λ).

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Revised 4.3.14