Essentials of Integration Theory for Analysis

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When the first edition of this textbook published in 2011, it constituted a substantial revision of the best-selling Birkh鋟ser 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: �2.5 and �3 have been substantially reworked. New topics have been added. As an application of the material about Hermite functions in �3.2, the author has added a brief introduction to Schwartz's theory of tempered distributions in �3.4. Section �4 is entirely new and contains applications, including the Central Limit Theorem, of Fourier analysis to measures. Related to this are subsections �2.5 and �2.6, where L関y's Continuity Theorem and Bochner's characterization of the Fourier transforms of Borel probability on RN 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.