Measure and Integral: An Introduction to Real Analysis (Chapman & Hall/CRC Pure and Applied Mathematics)

Zygmund, Antoni,Wheeden, Richard L.,Wheeden, Richard

ISBN 10: 0824764994 / ISBN 13: 9780824764999

Published by CRC Press, 1977

About this Item

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Bibliographic Details

• Title: Measure and Integral: An Introduction to Real Analysis (Chapman & Hall/CRC Pure and Applied Mathematics)
• Publisher: CRC Press
• Publication Date: 1977
• Language: English
• ISBN 10: 0824764994
• ISBN 13: 9780824764999
• Binding: Hardcover
• Condition: Good

About this title

Synopsis

This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given.

Closely related topics in real variables, such as functions of bounded variation, the Riemann-Stieltjes integral, Fubini's theorem, L(p)) classes, and various results about differentiation are examined in detail. Several applications of the theory to a specific branch of analysis--harmonic analysis--are also provided. Among these applications are basic facts about convolution operators and Fourier series, including results for the conjugate function and the Hardy-Littlewood maximal function.

Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis for student interested in mathematics, statistics, or probability. Requiring only a basic familiarity with advanced calculus, this volume is an excellent textbook for advanced undergraduate or first-year graduate student in these areas.

Review

. . .well written and authoritative.
---Choice

The style is characterized by its clarity and concreteness. . . . this work constitutes an excellent introductory textbook for those who wish to get acquainted with the modern methods of real variables.
---Mathematical Reviews