Real and Abstract Analysis: A Modern Treatment of the Theory of Functions of a Real Variable [Hardcover]

Editorial Reviews

About the Author

Edwin Hewitt

Edwinn Hewitt is a Professor of mathematics at the University of Washington, Seattle. He is the author of over 70 research papers and co-author, with K.A. Ross, of the book ABSTRACT HARMONIC ANALYSIS. He is a member of the National Research Council, U. S. A., has been visiting professor at Uppsala, Sweden, Yale University, and the Australian National University, Canberra. He has also lectured at many universities in the United States and Europe.

Karl Stromberg

Karl Stromberg is Professor of mathematics at Kansas State University. He has authored numerous research papers on analysis. He has been a member of the National Research Council, U.S.A. He received the Erstad Award as the outstanding teacher at the University of Oregon. He ahs spent visiting years at Yale University, the University of Chicago, Uppsala University (Sweden), and the University of York (England). He has lectured at many universities in the United States and in Europe. --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 476 pages
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K (December 31, 1975)
• Language: German
• ISBN-10: 3540901388
• ISBN-13: 978-3540901389
• Product Dimensions: 9.2 x 6.3 x 1.3 inches
• Shipping Weight: 1.8 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #10,492,750 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

10 of 10 people found the following review helpful:

5.0 out of 5 stars still one of the best, April 29, 2005

By 

wy-reader (USA) - See all my reviews

This review is from: Real and Abstract Analysis (Graduate Texts in Mathematics) (v. 25) (Hardcover)

After 30 years of its first publications, this book remains one of the best. It treats all the elements of a graduate course in analysis thoroughly. One of the few books that actually goes through construction of the real number system (in Chapter 1) and products of infinitely many measure spaces (in Chapter 6). There is plenty material to choose from, and all the standard topics are covered. In a very few cases notation is a bit cumbersome (or obsolete), but this is no big problem. Highly recommended to all graduate students in mathematics.

8 of 9 people found the following review helpful:

5.0 out of 5 stars Excellent real analysis reference, January 25, 2001

By 

Volker W. Elling (Stanford, CA United States) - See all my reviews

This review is from: Real and Abstract Analysis (Graduate Texts in Mathematics) (v. 25) (Hardcover)

In many applications today, such as PDE or harmonic analysis, it is crucial to have a really good grasp of the Lebesgue integral and absolutely continuous (rather than continuously differentiable) functions. Many real analysis books shy away from these matters.

Hewitt and Stromberg provide *every* detail, starting from scratch with measure theory, including Caratheodory's construction and fine distinctions such as Lebesgue vs. Lebesgue-Borel measurable sets. They proceed to discuss the Lebesgue integral in detail, then differentiation and absolutely continuous functions, the Lebesgue spaces including Riesz representation and a Banach space primer and finally integration on products (also infinite) of measure spaces. Fourier series and transforms are covered as well as fine details of (naive) set theory.

The book would be perfect if some standard analysis (Taylor series, analytic functions, Hospital rule, ...) was discussed; for this reason and because of its high level, it cannot be recommended as a book for 1st year calculus.

7 of 8 people found the following review helpful:

5.0 out of 5 stars One of the best references on the subject, April 4, 2000

By 

Bernardo Vargas - See all my reviews

This review is from: Real and Abstract Analysis (Graduate Texts in Mathematics) (v. 25) (Hardcover)

This is the kind of book I appreciate the most: one that's always got the information you need. This meticulous text covers thoroughly just every topic from elementary set theory up to product measures. It develops carefully all topics that should be included in standard analysis lectures (set theory, topology, Lebesgue integral, Banach and Hilbert spaces, differentiation, product measures) at such level of abstraction that the book turns out to be suitable for introductory courses, advanced courses, and later reference. The only one shortcoming I see is that the book includes no bibliography.

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