Chapter 52: Cardinal functions of measure theory

521
Basic theory

addμ and add** N**(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

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;
**m**_{countable} 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; *l*^{1}(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;

527
Skew products of ideals

** N**⧔

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

*L** ^{p}* and

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Revised 4.3.14