Foundations of real and abstract analysis Douglas S. Bridges

Format:

Book

Author/Creator:

Bridges, D. S. (Douglas S.), 1945-

Series:

Graduate texts in mathematics 174

Language:

English

Subjects (All):

Mathematical analysis.

Physical Description:

1 online resource

Place of Publication:

New York Springer ©1998

Language Note:

English

System Details:

text file PDF

Summary:

The core chapters of this volume provide a complete course on metric, normed, and Hilbert spaces, and include many results and exercises seldom found in texts on analysis at this level. The author covers an unusually wide range of material in a clear and concise format including elementary real analysis, Lebesgue integration on R, and an introduction to functional analysis. This makes a versatile text also suited for courses on real analysis, metric spaces, abstract analysis, and modern analysis. The book begins with a comprehensive chapter providing a fast-paced course on real analysis, and is followed by an introduction to the Lebesgue integral. This provides a reference for later chapters as well as an introduction for students with only the typical sequence of undergraduate calculus courses as prerequisites. Other features include a chapter introducing functional analysis, the Hahn-Banach theorem and duality, separation theorems, the Baire Category Theorem, the Open Mapping Theorem and their consequences, and unusual applications such as weak solutions of the Dirichlet Problem and Pareto optimality in Mathematical Economics. Of special interest is the unique collection of nearly 750 exercises, many with guidelines for their solutions. The exercises include applications and extensions of the main propositions and theorems, results that fill in gaps in proofs or that prepare for proofs later in the book, pointers to new branches of the subject, and difficult challenges for the very best students

Contents:

Cover

Preface

Contents

Introduction

1. Analysis on the Real Line

2. Differentition and the Lebesgue Integral

3. Analysis in Metric Spaces

4. Analysis in Normed Linear Spaces

5. Hilbert Spaces

6. An Introduction to Functional Analysis

Appendix A

Appendix B

Appendix C

References

Notes:

Includes bibliographical references (pages 311-315) and index

Print version record

Other Format:

Print version Bridges, D.S. (Douglas S.), 1945- Foundations of real and abstract analysis

ISBN:

0387226206

9780387226200

0585478198

9780585478197

9781461459613

1461459613

9781461459620

1461459621

128001010X

9781280010101

9786610010103

6610010102

OCLC:

559494450

Access Restriction:

Restricted for use by site license