Measure and Integration. 1st ed. 2019

種類:

電子ブック

責任表示:

by Satish Shirali, Harkrishan Lal Vasudeva

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2019

著者名:

• Shirali, Satish.
• Vasudeva, Harkrishan Lal.
• SpringerLink (Online service)

シリーズ名:

Springer Undergraduate Mathematics Series ;

ISBN:

9783030187477 [3030187470]    

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.

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