Essentials of integration theory for analysis
著者
書誌事項
Essentials of integration theory for analysis
（Graduate texts in mathematics, 262）
Springer Nature Switzerland AG, c2020
2nd ed
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注記
First ed.: Spribger Science+Business Media, LLC 2011
内容説明・目次
内容説明
When the first edition of this textbook published in 2011, it constituted a substantial revision of the best-selling Birkhauser title by the same author, A Concise Introduction to the Theory of Integration. Appropriate as a primary text for a one-semester graduate course in integration theory, this GTM is also useful for independent study. A complete solutions manual is available for instructors who adopt the text for their courses. This second edition has been revised as follows: 2.2.5 and 8.3 have been substantially reworked. New topics have been added. As an application of the material about Hermite functions in 7.3.2, the author has added a brief introduction to Schwartz's theory of tempered distributions in 7.3.4. Section 7.4 is entirely new and contains applications, including the Central Limit Theorem, of Fourier analysis to measures. Related to this are subsections 8.2.5 and 8.2.6, where Levy's Continuity Theorem and Bochner's characterization of the Fourier transforms of Borel probability on N are proven. Subsection 8.1.2 is new and contains a proof of the Hahn Decomposition Theorem. Finally, there are several new exercises, some covering material from the original edition and others based on newly added material.
目次
Preface.- Notation.- 1. The Classical Theory.-2. Measures. -3. Lebesgue Integration.-4. Products of Measures.-5. Changes of Variable.-6. Basic Inequalities and Lebesgue Spaces.-7. Hilbert Space and Elements of Fourier Analysis.-8. Radon-Nikodym, Hahn, Daniell Integration, and Caratheodory- Index.
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