Principles of Real Analysis / Edition 2

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1990 Hard cover 2nd ed. New. No dust jacket as issued. Sewn binding. Paper over boards. Audience: General/trade. slightly shelfworn & aged.

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The new, Third Edition of this successful text covers the basic theory of integration in a clear, well-organized manner. The authors present an imaginative and highly practical synthesis of the "Daniell method" and the measure theoretic approach. It is the ideal text for undergraduate and first-year graduate courses in real analysis.
This edition offers a new chapter on Hilbert Spaces and integrates over 150 new exercises. New and varied examples are included for each chapter. Students will be challenged by the more than 600 exercises. Topics are treated rigorously, illustrated by examples, and offer a clear connection between real and functional analysis.
This text can be used in combination with the authors' Problems in Real Analysis, 2nd Edition, also published by Academic Press, which offers complete solutions to all exercises in the Principles text.
Key Features:
* Gives a unique presentation of integration theory
* Over 150 new exercises integrated throughout the text
* Presents a new chapter on Hilbert Spaces
* Provides a rigorous introduction to measure theory
* Illustrated with new and varied examples in each chapter
* Introduces topological ideas in a friendly manner
* Offers a clear connection between real analysis and functional analysis
* Includes brief biographies of mathematicians
"All in all, this is a beautiful selection and a masterfully balanced presentation of the fundamentals of contemporary measure and integration theory which can be grasped easily by the student."
--J. Lorenz in Zentralblatt für Mathematik
"...a clear and precise treatment of the subject. There are many exercises of varying degreesof difficulty. I highly recommend this book for classroom use."
--CASPAR GOFFMAN, Department of Mathematics, Purdue University

Audience: Upper-level graduate or undergraduate students studying real analysis.

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Editorial Reviews

Textbook for senior undergraduate and first-year graduate courses. Assumes familiarity with advanced calculus and fundamental algebraic concepts. Covers the basic theory of integration using a practical synthesis of the "Daniell method" and the measure-theoretic approach. Corrected and slightly amended from the first edition (1981). Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780120502554
  • Publisher: Elsevier Science & Technology Books
  • Publication date: 2/28/1990
  • Edition description: Older Edition
  • Edition number: 2
  • Pages: 304
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.80 (d)

Table of Contents

Ch. 1 Fundamentals of Real Analysis 1
Ch. 2 Topology and Continuity 57
Ch. 3 The Theory of Measure 93
Ch. 4 The Lebesgue Integral 161
Ch. 5 Normed Spaces and L[subscript p]-Spaces 217
Ch. 6 Hilbert Spaces 275
Ch. 7 Special Topics in Integration 325
Bibliography 399
List of Symbols 401
Index 403
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