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题名/责任者:

Measure theory / Donald L. Cohn.

版本说明:

2nd ed.

出版发行项:

[北京 : 世界图书出版公司, 2017.]

ISBN:

9781461469551

ISBN:

1461469554

ISBN:

9787519224134

载体形态项:

xxi, 457 pages : illustrations ; 23 cm.

变异题名:

测度论

丛编说明:

Birkha?user advanced texts

丛编统一题名:

Birkha?user advanced texts.

个人责任者:

Cohn, Donald L., 1942-

论题主题:

Measure theory.

中图法分类号:

O174.12

一般附注:

Chinese title on cover.

书目附注:

Includes bibliographical references (pages 439-443) and indexes.

内容附注:

1. Measures -- 2. Functions and integrals -- 3. Convergence -- 4. Signed and complex measures -- 5. Product measures -- 6. Differentiation -- 7. Measures on locally compact spaces -- 8. Polish spaces and analytic sets -- 9. Haar measure -- A. Notation and set theory -- B. Algebra -- C. Calculus and topology in Rd[supercript] -- D. Topological spaces and metric spaces -- E. The Bochner integral -- F. Liftings -- G. The Banach-Tarski paradox -- H. The Henstock-Kurzweil and McShane integrals.

摘要附注:

New edition provides additional topics such as the Kurzweil-Henstock integral, Banach-Tasrki paradox, a proof of the existence of liftings, the Daniell integral, and a brief introduction to measure-theoretic probability theory. Contains numerous examples and exercises. Provides a solid background for study in harmonic analysis and probability theory. Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings. Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.

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