Elements of the Theory of Functions and Functional Analysis (Paperback)

by A. N. Kolmogorov (Author), S. V. Fomin (Author)

Editorial Reviews

Product Description
Based on the authors’ courses and lectures, this two-volume advanced-level text is now available in a single volume. Topics include metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque interval, Hilbert Space and more. Each section contains exercises. Lists of symbols, definitions and theorems. 1957 ed.

Product Details

• Paperback: 288 pages
• Publisher: Dover Publications (February 16, 1999)
• Language: English
• ISBN-10: 0486406830
• ISBN-13: 978-0486406831
• Product Dimensions: 8.2 x 5.4 x 0.6 inches
• Shipping Weight: 9.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.9 out of 5 stars See all reviews (14 customer reviews)
• Amazon.com Sales Rank: #23,271 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

56 of 60 people found the following review helpful:

5.0 out of 5 stars Still one of the finest., July 28, 2000

By	Bernardo Vargas (Weimar, Germany) - See all my reviews

This highly regarded book came out from the notes of Andrei Kolmogorov's lectures given at Moscow's Lomonosov University in the 1940's, and it still stands as one of the best introductions to real analysis available.

The authors introduce step by step all the key concepts needed to get a thorough understanding of the subject and proceed all the way long from set theory to Fredholm integral equations.

This book is appreciated not only because the topics it includes but mostly because of the insight with which it was written. It is a pleasure to find through every page of the book the great genious of Kolmogorov who not only mastered most areas of mathematics but who also had an almost unparalleled understanding of what the trends of future mathematics would be.

The contents are: Elements of Set Theory; Metric and Topological Spaces; Normed and Topological Linear Spaces; Linear Functionals and Linear Operators; Elements of Differential Calculus in Linear Spaces; Measure, Measurable Functions, Integral; Indefinite Lebesgue Integral, Differentiation Theory; Spaces of Summable Functions; Trigonometric Series, Fourier Transformation; Linear Integral Equations.

Full motivation and detailed explanation for each topic. Short bibliography, but that is justified by the fact that the authors themselves were involved in the development of the topics covered.

Conclusion: a must-have text for every mathematician or math student.

26 of 26 people found the following review helpful:

5.0 out of 5 stars A MAGNIFIC BOOK !, November 18, 1999

By	Paulo ([e-mail]) (Brazil) - See all my reviews

This book is divided into two parts. The first part is devoted mainly to metric and normed spaces. There are too a chapter on the essentials of set theory, an addendum on generalized functions, and a chapter on linear operators. The second part is devoted to measure theory, the Lebesgue integral, the theory of square integrable functions(L2) and Hilbert spaces. The second part incorporates exercises to the reader. The clarity of exposition and the elegancy of this book is notorious ! This book can be recommended not only for mathematicians, but for theoretical physicists. Do you know why the Heisenberg picture of quantum mechanics is equivalent to the Schrodinger picture of quantum mechanics ? Mathematically, Heisenberg theory uses the space l2, while Schrodinger theory uses the space L2. A consequence of the Riesz-Fisher theorem is that the spaces l2 and L2 are isomorphic, a result proved in this book. The two theories leads to the same physical results, and in consequence are equivalent, although different in the mathematical content ! You need to buy this book !

28 of 29 people found the following review helpful:

4.0 out of 5 stars Great book, fair reprint, March 29, 2000

By	Pedro L. Ribeiro "lqp-man" (Cotia, SP Brazil) - See all my reviews (REAL NAME)

I must say that Kolmogorov is one of my favorite Russian scientists and scientific writers (the others are Arnol'd, Gel'fand and Landau). His approach over real and functional analysis is superb. But I have a serious complaint: why did Dover choose the old and dated Graylock edition to reprint this masterpiece? The most recent Russian edition has a lot of other important topics (missing in Dover's reprint), such as differential calculus in Banach spaces, which is so difficult to find a decent treatment of. The organization of the book is also better in the Russian edition. A good revised and translated reprint of it would deserve not five, but six, seven, ten stars...