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.

Key Features

@bul:* 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


Upper-level graduate or undergraduate students studying real analysis.

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 Bibliography


No. of pages:
© 1999
Academic Press
Print ISBN:
Electronic ISBN:

About the authors

Owen Burkinshaw

Affiliations and Expertise

Indiana University-Purdue University, Indianapolis , U.S.A.

Charalambos Aliprantis

Affiliations and Expertise

Purdue University, Indianapolis, U.S.A.


"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 FUR MATEMATIK "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