An in-depth look at real analysis and its applications-now expanded and revised.

This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory.

This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include:

* Revised material on the n-dimensional Lebesgue integral.

* An improved proof of Tychonoff's theorem.

* Expanded material on Fourier analysis.

* A newly written chapter devoted to distributions and differential equations.

* Updated material on Hausdorff dimension and fractal dimension.

Table of Contents

0 Prologue

1. Measures

2 Integration

3 Signed Measures and Diferentiation

4 Point Set Topology

5 Elements of Functional Analysis

6 L Ap Spaces

7 Radon Measures

8 Elements of Fourier Analysis

9 Elements of Distribution Theory

10 Topics in Probability Theory

11 More Measures and Integrals

About the Author

Gerald B. Folland  is Professor of Mathematics at the University of Washington in Seattle. He has written extensively on mathematical analysis, including Fourier analysis, harmonic analysis, and differential equations.