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Theory of Functions of a Real Variable, by Isidor Pavlovich Natanson
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Originally published in two volumes, this long out-of-print work by a prominent Soviet mathematician presents a thorough examination of the theory of functions of a real variable. Intended for advanced undergraduates and graduate students of mathematics, the treatment offers a clear account of integration theory and a practical introduction to functional analysis. Prerequisites include a background in the foundations of elementary analysis and some familiarity with the theory of irrational numbers, the theory of limits, continuous functions, Riemann integrals, and infinite series.
Volume I covers infinite and point sets, measurable sets and functions, the Lebesgue integral of a bounded function, square-summable functions, functions of finite variations, the Stieltjes integral, absolutely contiguous functions, and the indefinite Lebesgue integral. Volume II addresses singular integrals, trigonometric series, convex functions, point sets in two-dimensional space, measurable functions of several variables and their integration, set functions and their applications in the theory of integration, transfinite numbers, the Baire classification, certain generalizations of the Lebesgue integral, and some ideas from functional analysis. Many chapters feature challenging exercises.
- Sales Rank: #3202561 in Books
- Published on: 2013-03-30
- Original language: English
- Number of items: 1
- Dimensions: 9.02" h x .58" w x 5.98" l, .82 pounds
- Binding: Paperback
- 276 pages
About the Author
Soviet mathematician Isidor Pavlovich Natanson (1906–64) was affiliated with St. Petersburg State University. He also wrote a three-volume treatise, Constructive Function Theory.
Most helpful customer reviews
7 of 7 people found the following review helpful.
The best book in real variables I ever met
By Pavel B. Dubovski
The best book in real variables I ever met. A lot of various information forms a deep understanding of the subject. Some parts may be skipped during the first reading.
9 of 10 people found the following review helpful.
well written, clear presentation
By Y. Chen
When asked about the best book on analysis, my much older research colleague who went through a traditional, rigorous training in the 60's immediately mentioned the name Natanson. I'm glad I got this book. It's refreshing to read a mathematics book written half a century ago. People then knew how to write and wrote for a clear-minded audience. The presentation is succinct but not abstruse (unlike Hardy's book on Inequalities). I found the exercises at the end of each chapter to be quite difficult.
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