Hardcover ISBN:  9781470410995 
Product Code:  SIMON/1 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470427559 
Product Code:  SIMON/1.E 
List Price:  $95.00 
MAA Member Price:  $85.50 
AMS Member Price:  $76.00 
Hardcover ISBN:  9781470410995 
eBook: ISBN:  9781470427559 
Product Code:  SIMON/1.B 
List Price:  $194.00 $146.50 
MAA Member Price:  $174.60 $131.85 
AMS Member Price:  $155.20 $117.20 
Hardcover ISBN:  9781470410995 
Product Code:  SIMON/1 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470427559 
Product Code:  SIMON/1.E 
List Price:  $95.00 
MAA Member Price:  $85.50 
AMS Member Price:  $76.00 
Hardcover ISBN:  9781470410995 
eBook ISBN:  9781470427559 
Product Code:  SIMON/1.B 
List Price:  $194.00 $146.50 
MAA Member Price:  $174.60 $131.85 
AMS Member Price:  $155.20 $117.20 

Book Details2015; 789 ppMSC: Primary 26; 28; 42; 46; Secondary 33; 35; 41; 52; 54; 60
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a fivevolume set that can serve as a graduatelevel analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis.
Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and \(L^p\) spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, spacefilling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.
ReadershipResearchers (mathematicians and some applied mathematicians and physicists) using analysis, professors teaching analysis at the graduate level, graduate students who need any kind of analysis in their work.
This item is also available as part of a set: 
Table of Contents

Chapters

Chapter 1. Preliminaries

Chapter 2. Topological spaces

Chapter 3. A first look at Hilbert spaces and Fourier series

Chapter 4. Measure theory

Chapter 5. Convexity and Banach spaces

Chapter 6. Tempered distributions and the Fourier transform

Chapter 7. Bonus chapter: Probability basics

Chapter 8. Bonus chapter: Hausdorff measure and dimension

Chapter 9. Bonus chapter: Inductive limits and ordinary distributions


Additional Material

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A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a fivevolume set that can serve as a graduatelevel analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis.
Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and \(L^p\) spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, spacefilling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.
Researchers (mathematicians and some applied mathematicians and physicists) using analysis, professors teaching analysis at the graduate level, graduate students who need any kind of analysis in their work.

Chapters

Chapter 1. Preliminaries

Chapter 2. Topological spaces

Chapter 3. A first look at Hilbert spaces and Fourier series

Chapter 4. Measure theory

Chapter 5. Convexity and Banach spaces

Chapter 6. Tempered distributions and the Fourier transform

Chapter 7. Bonus chapter: Probability basics

Chapter 8. Bonus chapter: Hausdorff measure and dimension

Chapter 9. Bonus chapter: Inductive limits and ordinary distributions