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Theory of Functions of a Real Variable

Isidor Pavlovich Natanson

ISBN 10: 1258648318 / ISBN 13: 9781258648312
Published by Literary Licensing, LLC, 2013
Condition: Good Soft cover
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Bibliographic Details

Title: Theory of Functions of a Real Variable

Publisher: Literary Licensing, LLC

Publication Date: 2013

Binding: Paperback

Book Condition: Good

About this title

Synopsis:

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.

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. 

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