Real Analysis: Part 1: A Comprehensive Course in Analysis: A Comprehensive Course in Analysis, Part 1 - Hardcover

Simon, Barry

Hardcover

ISBN 10: 1470410990 ISBN 13: 9781470410995

Publisher: American Mathematical Society, 2015

Synopsis

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.

About this title

About the Author

Barry Simon, California Institute of Technology, Pasadena, CA, USA.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2015
• Language: English
• ISBN 10: 1470410990
• ISBN 13: 9781470410995
• Binding: Hardcover
• Number of pages: 789