| 期刊全称 | A Course on Integration Theory | | 期刊简称 | including more than | | 影响因子2023 | Nicolas Lerner | | 视频video | http://file.papertrans.cn/141/140521/140521.mp4 | | 发行地址 | Includes over 150 exercises with detailed solutions.Requires no prior knowledge of advanced mathematics although the results proven in the book are not elementary.Is self-contained, providing detailed | | 图书封面 |  | | 影响因子 | 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. The Radon-Nikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems, including Marcinkiewicz‘s theorem, the definition of Lebesgue points and Lebesgue differentiation theorem are further topics included. A detailed appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. The appendix also provides more advanced material such as some basic properties of cardinals and ordinals which are useful in the study of measu | | Pindex | Textbook 2014 |
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