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Measure and Integration

✍ Scribed by Satish Shirali, Harkrishan Lal Vasudeva

Publisher
Springer International Publishing
Year
2019
Tongue
English
Leaves
609
Series
Springer Undergraduate Mathematics Series
Edition
1st ed. 2019
Category
Library
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✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xii
Preliminaries (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 1-42
Measure in Euclidean Space (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 43-108
Measure Spaces and Integration (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 109-162
Fourier Series (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 163-209
Differentiation (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 211-336
Lebesgue Spaces and Modes of Convergence (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 337-374
Product Measure and Completion (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 375-404
Hints (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 405-590
Back Matter ....Pages 591-598

✦ Subjects

Mathematics; Measure and Integration; Real Functions; Fourier Analysis; Functional Analysis

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