Measure and Integral An Introduction to Real Analysis | Edition: 1
Author: Richard Wheeden, Richard L. Wheeden, Antoni Zygmund
publisher: Taylor & Francis
publisher Date: 11/01/1977
Schools: Temple University，Wayne State University，University of Chicago，Georgia Institute of Techology，College of William and Mary，Vanderbilt University，Colorado School of Mines，University of Colorado at Boulder，Wright State University
Description: 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 analysisharmonic analysisare 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.