Measure and Integral: An Introduction to Real Analysis

by Richard L. Wheeden, Antoni Zygmund

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.

Genres: Mathematics, Technical

288 pages, Hardcover

First published November 1, 1977

Reviews

[Nick · Rating 5 out of 5]

Compact but insightful with pleasant notation. The choice to consider only Euclidean spaces initially and introduce abstract measures later is interesting. I'm not sure how I feel about it.

[Ghulam Murtaza · Rating 4 out of 5]

This is a very good book on Lebesgue measure theory. Actually this book is recommended to me by my supervisor.