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Real Analysis - A Comprehensive Course in Analysis, Part 1

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Author(s): Barry Simon
Series: A Comprehensive Course in Analysis
Publisher: American Mathematical Society
Year: 2015

Language: English
Pages: 811

Cover......Page 1
Title page......Page 4
Contents......Page 8
Preface to the series......Page 12
Preface to Part 1......Page 18
Chapter 1. Preliminaries......Page 22
Chapter 2. Topological spaces......Page 56
Chapter 3. A first look at Hilbert spaces and Fourier series......Page 128
Chapter 4. Measure theory......Page 206
Chapter 5. Convexity and Banach spaces......Page 376
Chapter 6. Tempered distributions and the Fourier transform......Page 514
Chapter 7. Bonus chapter: Probability basics......Page 636
Chapter 8. Bonus chapter: Hausdorff measure and dimension......Page 700
Chapter 9. Bonus chapter: Inductive limits and ordinary distributions......Page 726
Bibliography......Page 734
Symbol index......Page 786
Subject index......Page 790
Author index......Page 800
Index of capsule biographies......Page 810
Back Cover......Page 811