Theory Of Functions Of A Real Variable is a comprehensive textbook written by Isidor Pavlovich Natanson. The book covers various topics related to real analysis, including the theory of functions of a real variable, limits, continuity, differentiation, integration, and sequences and series of functions. It provides a thorough introduction to the subject, starting with the basic concepts and gradually building up to more advanced topics.The book is divided into four parts, each of which covers a different aspect of real analysis. Part one focuses on the foundations of the subject, including sets, functions, and the real number system. Part two covers the theory of limits, continuity, and differentiability, while part three delves into the theory of integration and its applications. Finally, part four covers sequences and series of functions, including power series and Fourier series.Throughout the book, Natanson provides clear explanations of the concepts and theorems, with numerous examples and exercises to help readers understand the material. The book is aimed at advanced undergraduate and graduate students in mathematics, as well as researchers and professionals in the field of real analysis. It is a valuable resource for anyone looking to deepen their understanding of the subject.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.
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.
Dover republication of the F. Ungar Publishing Company, New York, 1955 (Volume I) and 1960 (Volume II) editions.
www.doverpublications.com
