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＜電子ブック＞
Measure and Integration / by Satish Shirali, Harkrishan Lal Vasudeva
(Springer Undergraduate Mathematics Series. ISSN:21974144)

版	1st ed. 2019.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2019
大きさ	XII, 598 p : online resource
著者標目	*Shirali, Satish author Vasudeva, Harkrishan Lal author SpringerLink (Online service)
件　名	LCSH:Measure theory LCSH:Functions of real variables LCSH:Fourier analysis LCSH:Functional analysis FREE:Measure and Integration FREE:Real Functions FREE:Fourier Analysis FREE:Functional Analysis
一般注記	1 Preliminaries -- 2 Measure in Euclidean Space -- 3 Measure Spaces and Integration -- 4 Fourier Series -- 5 Differentiation -- 6 Lebesgue Spaces and Modes of Convergence -- 7 Product Measure and Completion -- 8 Hints -- References -- Index This textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis. Proceeding at a leisurely, student-friendly pace, the authors begin by recalling elementary notions of real analysis before proceeding to measure theory and Lebesgue integration. Further chapters cover Fourier series, differentiation, modes of convergence, and product measures. Noteworthy topics discussed in the text include Lp spaces, the Radon–Nikodým Theorem, signed measures, the Riesz Representation Theorem, and the Tonelli and Fubini Theorems. This textbook, based on extensive teaching experience, is written for senior undergraduate and beginning graduate students in mathematics. With each topic carefully motivated and hints to more than 300 exercises, it is the ideal companion for self-study or use alongside lecture courses HTTP:URL=https://doi.org/10.1007/978-3-030-18747-7

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