A Course on Integration Theory : including more than 150 exercises with detailed answers
- 種類:
- 電子ブック
- 責任表示:
- by Nicolas Lerner
- 出版情報:
- Basel : Springer Basel : Imprint: Birkhäuser, 2014
- 著者名:
- ISBN:
- 9783034806947 [3034806949]
- 注記:
- This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathéodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change-of-variables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality, are proven. Further topics include the Radon-Nikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems including Marcinkiewicz's theorem, and the definition of Lebesgue points and the Lebesgue differentiation theorem. Each chapter ends with a large number of exercises and detailed solutions. A comprehensive appendix provides the reader with various elements
- ローカル注記:
- 学内専用E-BOOKS (local access only)
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