About this book
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.
Measure theory Integration theory Lebesgue measure Fourier series Fubini theorem Tonelli theorem Lp spaces Vitali covering theorem Radon-Nikodym theorem Product measure Cantor set Bounded variation Absolute continuity
- DOI https://doi.org/10.1007/978-3-030-18747-7
- Copyright Information Springer Nature Switzerland AG 2019
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-3-030-18746-0
- Online ISBN 978-3-030-18747-7
- Series Print ISSN 1615-2085
- Series Online ISSN 2197-4144
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