Principles of Real Analysis / Edition 3

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With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.

• 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

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

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Editorial Reviews

From the Publisher
"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."

"A clear and precise treatment of the subject. All details are given in the text...I used a portion of the book on extension of measures and product measures in a graduate course in real analysis. There are many exercises of varying degrees of difficulty. I highly recommend this book for classroom use."
-CASPAR GOFFMAN, Department of Mathematics, Purdue University

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: 9780120502578
  • Publisher: Elsevier Science
  • Publication date: 9/9/1998
  • Edition description: REV
  • Edition number: 3
  • Pages: 415
  • Product dimensions: 0.94 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Fundamentals of Real Analysis
Topology and Continuity
The Theory of Measure
The Lebesgue Integral
Normed Spaces and Lp-Spaces
Hilbert Spaces
Special Topics in Integration

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Sort by: Showing all of 3 Customer Reviews
  • Anonymous

    Posted September 11, 2002

    Great Real Analysis Book

    This is one of the best books I have seen in real analysis. It has "almost" (nothing is perfect,right) everything what you need as a graduate student. The presentation is well done, with very detailed proofs. I also do not agree with first reviewer because the book DOES contain all important theorems and definitions. The chapters the books contains is probably what a first year graduate student should have, and the problems go very good with the text, becuase some are easier and some are quite challenging. This book is excellent if you are preparing for qual. exams because solutions in the problem book (seperate from this book) are excellent. They are presented in a very detailed manner and it really makes you learn real analysis IF YOU WANT TO. So, I would recommend this book along with Rudin's three books on analysis, of course.

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  • Anonymous

    Posted September 11, 2002

    Well crafted texbook

    This is an exceptionally well crafted textbook on Real Analysis. It is carefully executed and is delightfully clear. I use this textbook as a reference in my graduate Mathematical Economics class. I find that students are very happy with the exposition of the material and that they find the texbook very useful. I highly recommend this textbook.

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  • Anonymous

    Posted October 19, 2000

    one of the best in the field

    This is a book for those who have to learn Real Analysis for the first time. The exposition is complete and very clear. I cannot agree with the first reviewer at all, and I do not know what text would that reviewer recommend. There are many texts in this field, but this one remains one of my most favorite as I use it frequently as a reference. Highly recommended.

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