Measure and integral : an introduction to real analysis / Richard L. Wheeden and Antoni Zygmund.

Includes index.

Chapter 1 Preliminaries;
Chapter 2 Functions of Bounded Variation and the Riemann-Stieltjes Integral;
Chapter 3 Lebesgue Measure and Outer Measure;
Chapter 4 Lebesgue Measurable Functions;
Chapter 5 The Lebesgue Integral;
Chapter 6 Repeated Integration;
Chapter 7 Differentiation;
Chapter 8 Lp Classes;
Chapter 9 Approximations of the Identity and Maximal Functions;
Chapter 10 Abstract Integration.
Chapter 11 Outer Measure and Measure
Chapter 12 A Few Facts from Harmonic Analysis;
Chapter 13 The Fourier Transform;
Chapter 14 Fractional Integration;
Chapter 15 Weak Derivatives and Poincaré-Sobolev Estimates; Notations;
Index.

This book provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content.Published nearly forty years after the first edition, this long-awaited Second Edition also:Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 p Shows the Hilbert transform to be a bounded operator on L2, as.