*Chapter 21: Taxonomy of measure spaces

211
Definitions

Complete, totally finite, σ-finite, strictly localizable,
semi-finite, localizable, locally determined measure spaces; atoms;
elementary relationships; countable-cocountable measures.

212
Complete spaces

Measurable and integrable functions on complete spaces; completion of
a measure.

213
Semi-finite, locally determined and localizable spaces

Integration on semi-finite spaces; c.l.d. versions; measurable
envelopes; characterizing localizability and strict localizability.

214
Subspaces

Subspace measures on arbitrary subsets; integration; direct sums of
measure spaces; *extending measures to well-ordered families of sets.

215
σ-finite spaces and the principle of exhaustion

The principle of exhaustion; characterizations of
σ-finiteness; the intermediate value theorem for atomless
measures.

*216
Examples

A complete localizable non-locally-determined space; a complete
locally determined non-localizable space; a complete locally
determined localizable space which is not strictly localizable.

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Revised 3.8.15