Measure and Integral

Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis 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 L^p, 1 < p< 2
• Shows the Hilbert transform to be a bounded operator on L², as an application of the L² theory of the Fourier transform in the one-dimensional case
• Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of H¿lder continuous functions and t