Measure Theory, Volume 2 - Broad Foundations.pdf

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电子书籍 【ISBN】 0953812928  【作者】 D. H. Fremlin
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Contents General Introduction 9 Introduction to Volume 2 10 *Chapter 21: Taxonomy of measure spaces Introduction 12 211 De nitions 12 Complete, totally nite, ? nite, strictly localizable, semi- nite, localizable, locally determined measure spaces; atoms; elementary relationships; countable-cocountable measures. 212 Complete spaces 18 Measurable and integrable functions on complete spaces; completion of a measure. 213 Semi- nite, locally determined and localizable spaces 24 Integration on semi- nite spaces; c.l.d. versions; measurable envelopes; characterizing localizability, strict localizability, ? niteness. 214 Subspaces 36 Subspace measures on arbitrary subsets; integration; direct sums of measure spaces. 215 ? nite spaces and the principle of exhaustion 43 The principle of exhaustion; characterizations of ? niteness; the intermediate value theorem for atomless measures. *216 Examples 47 A complete localizable non-locally-determined space; a complete locally d……

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