Real analysis

Author(s)

• Simon, Barry

Bibliographic Information

Real analysis

Barry Simon

（A comprehensive course in analysis, pt. 1）

American Mathematical Society, c2015

Note

Includes bibliographical references and indexes

Description and Table of Contents

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.

Table of Contents

Preliminaries Topological spaces A first look at Hilbert spaces and Fourier series Measure theory Convexity and Banach spaces Tempered distributions and the Fourier transform Bonus chapter: Probability basics Bonus chapter: Hausdorff measure and dimension Bonus chapter: Inductive limits and ordinary distributions Bibliography Symbol index Subject index Author index Index of capsule biographies

by "Nielsen BookData"

Details

• NCID: BB20268244
• ISBN:
  • 9781470410995
• LCCN: 2014047381
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R.I.
• Pages/Volumes: xx, 789 p.
• Size: 27 cm
• Classification:
  • LCC : QA300
  • DC23 : 515/.8
• Subject Headings:
  • LCSH : Mathematical analysis -- Textbooks
• Parent Bibliography ID:
  • BB20268142