Theory of Functions of a Real Variable (Dover Books on Mathematics)

Bagemihl, Frederick

ISBN 10: 048680643X / ISBN 13: 9780486806433

Published by Dover Publications Inc., 2016

About this Item

Most items will be dispatched the same or the next working day. An apparently unread copy in perfect condition. Dust cover is intact with no nicks or tears. Spine has no signs of creasing. Pages are clean and not marred by notes or folds of any kind.

Seller Inventory # rev3490054173

Bibliographic Details

• Title: Theory of Functions of a Real Variable (Dover Books on Mathematics)
• Publisher: Dover Publications Inc.
• Publication Date: 2016
• Language: English
• ISBN 10: 048680643X
• ISBN 13: 9780486806433
• Binding: paperback
• Condition: Like New
• Weight: 779 grams

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.