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Foundations of Real and Abstract Analysis : Graduate Texts In Mathematics - Douglas S. Bridges

Foundations of Real and Abstract Analysis

Graduate Texts In Mathematics

Hardcover Published: 23rd October 1997
ISBN: 9780387982397
Number Of Pages: 322

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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.

Introductionp. 1
Real Analysisp. 9
Analysis on the Real Linep. 11
Differentiation and the Lebesgue Integralp. 79
Abstract Analysisp. 123
Analysis in Metric Spacesp. 125
Analysis in Normed Linear Spacesp. 173
Hilbert Spacesp. 233
An Introduction to Functional Analysisp. 259
What Is a Real Number?p. 291
Axioms of Choice and Zorn's Lemmap. 299
Pareto Optimalityp. 303
Referencesp. 311
Indexp. 317
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387982397
ISBN-10: 0387982396
Series: Graduate Texts In Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 322
Published: 23rd October 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.13 x 15.88  x 1.91
Weight (kg): 0.61