Real Analysis: A Comprehensive Course in Analysis, Part 1 by Barry Simon (PDF)

Description

A Comprehensive Course in Analysis by Poincare Prize winner Barry Simon is a five-volume set that can serve as a graduate-level 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, Frechet 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, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.

User’s Reviews

Editorial Reviews: About the Author Barry Simon, California Institute of Technology, Pasadena, CA, USA.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is so difficult to read that I feel sorry for the students that studied using itIt is made for mathematicians that already know the subject. There are interesting bits regarding the history of some theorems and about the life of some mathematiciansBut the definitions are introduced without any motivation. The reader may wonder; are all those hypotheses necessary. What is the use of this theorem?Too expensive. I have the first volume and will not buy the others. There are better books in the market

⭐Written by an amateur not a mathematicianI found mistakes in the definitions and proofsThis is not a good or average text . It’s a wonderful example for a well printed and stylish book with stupid content

⭐This is an excellent work by the master.

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