Measure theory  v. 1 ~ v. 2

V.I. Bogachev

Measure theory is a classical area of mathematics born more than two thousand years ago. Nowadays it continues intensive development and has fruitful connections with most other fields of mathematics as well as important applications in physics. This book gives an exposition of the foundations of modern measure theory and offers three levels of presentation such as: a standard university graduate course, an advanced study containing some complements to the basic course (the material of this level corresponds to a variety of special courses), and, finally, more specialized topics partly covered by more than 850 exercises. Volume 1 (Chapters 1-5) is devoted to the classical theory of measure and integral. Whereas the first volume presents the ideas that go back mainly to Lebesgue, the second volume (Chapters 6-10) is to a large extent the result of the later development up to the recent years. The central subjects in Volume 2 are: transformations of measures, conditional measures and weak convergence of measures. These three topics are closely interwoven and form the heart of modern measure theory. The organization of the book does not require systematic reading from beginning to end; in particular, almost all sections in the supplements are independent of each other and are directly linked only to specific sections of the main part. The target readership includes graduate students interested in deeper knowledge of measure theory, instructors of courses in measure and integration theory, and researchers in all fields of mathematics. The book may serve as a source for many advanced courses or as a reference.

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[目次]

  • Constructions and extensions of measures.- The Lebesgue integral.- Operations on measures and functions.- The spaces Lp and spaces of measures.- Connections between the integral and derivative.- Borel, Baire and Souslin sets.- Measures on topological spaces.- Weak convergence of measure.- Transformations of measures and isomorphisms.- Conditional measures and conditional.

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この本の情報

書名 Measure theory
著作者等 Bogachev, V. I.
Bogachev Vladimir
巻冊次 v. 1
v. 2
出版元 Springer
刊行年月 2007
ページ数 2 v.
大きさ 25 cm
ISBN 3540345132
NCID BA79637027
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言語 英語
出版国 ドイツ
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