Measure and Integral: An Introduction to Real Analysis, 2nd Edition

Book Description

Now considered a classic text on the topic, Measure and Integral: An Introduction to Real provides an introduction to by first developing the of measure and 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 < 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 Hölder continuous functions and the space of functions of bounded mean oscillation
  • Derives a subrepresentation formula, which in higher dimensions plays a role roughly similar to the one played by the fundamental theorem of calculus in one dimension
  • Extends the subrepresentation formula derived for smooth functions to functions with a weak gradient
  • Applies the norm estimates derived for fractional integral operators to obtain local and global first-order Poincaré–Sobolev inequalities, including endpoint cases
  • Proves the existence of a tangent plane to the of a Lipschitz function of several variables
  • Includes many new exercises not present in the first edition

This widely used and highly respected text for upper-division undergraduate and first-year graduate students of mathematics, statistics, probability, or is revised for a new generation of students and instructors. The book also serves as a handy reference for professional mathematicians.

Book Details

  • Title: Measure and Integral: An Introduction to Real Analysis, 2nd Edition
  • Author:
  • Length: 532 pages
  • Edition: 2
  • Language: English
  • Publisher:
  • Publication Date: 2015-04-24
  • ISBN-10: 1498702899
  • ISBN-13: 9781498702898
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