Essentials of Integration Theory for Analysis. 2nd ed. 2020

種類:

電子ブック

責任表示:

by Daniel W. Stroock

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Stroock, Daniel W.
• SpringerLink (Online service)

シリーズ名:

Graduate Texts in Mathematics ; 262

ISBN:

9783030584788 [303058478X]    

注記:

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 Carathéodory- Index.
When the first edition of this textbook published in 2011, it constituted a substantial revision of the best-selling Birkhäuser 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 Lévy's Continuity Theorem and Bochner's characterization of the Fourier transforms of Borel probability on ℝ

ローカル注記:

学内専用E-BOOKS (local access only)