Contents of Measure Theory, by D.H.Fremlin

*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