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.
Product Identifiers
Publisher
Dover Publications Inc.
ISBN-13
9780486806433
eBay Product ID (ePID)
224563749
Product Key Features
Author
I.P. Natanson
Publication Name
Theory of Functions of a Real Variable
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
2016
Type
Textbook
Number of Pages
560 Pages
Dimensions
Item Height
234mm
Item Width
156mm
Additional Product Features
Title_Author
I.P. Natanson
Country/Region of Manufacture
United States
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