Real Analysis : Measure Theory, Integration, and Hilbert Spaces / Rami Shakarchi, Elias M. Stein.

Format:

Book

Author/Creator:

Stein, Elias M., Author.

Shakarchi, Rami, Author.

Series:

Princeton lectures in analysis ; 3

Language:

English

Subjects (All):

Functional analysis.

Measure theory.

Integrals, Generalized.

Physical Description:

1 online resource (423 p.)

Place of Publication:

Princeton, NJ : Princeton University Press, 2005

Language Note:

English

Summary:

Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. Also available, the first two volumes in the Princeton Lectures in Analysis:

Contents:

Frontmatter

Foreword

Contents

Introduction

1 Measure Theory

2 Integration Theory

3 Differentiation and Integration

4 Hilbert Spaces: An Introduction

5 Hilbert Spaces: Several Examples

6 Abstract Measure and Integration Theory

7 Hausdorff Measure and Fractals

Notes and References

Bibliography

Symbol Glossary

Index

Notes:

Description based upon print version of record

Includes bibliographical references (pages 389-393) and index

Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Nov 2019)

ISBN:

9786612936364

9786612473128

9781282473126

1282473123

9781282936362

1282936360

9781400835560

1400835569

OCLC:

647843248