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Measure and Integral: An Introduction to Real Analysis, Second Edition

Measure and Integral: An Introduction to Real Analysis, Second Edition

          
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About the Book

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 Lp, 1 p
  • 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 graph 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 engineering is revised for a new generation of students and instructors. The book also serves as a handy reference for professional mathematicians.


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Product Details
  • ISBN-13: 9781032918938
  • Publisher: Taylor & Francis Ltd
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 984 gr
  • ISBN-10: 1032918934
  • Publisher Date: 14 Oct 2024
  • Height: 234 mm
  • No of Pages: 532
  • Sub Title: An Introduction to Real Analysis, Second Edition
  • Width: 156 mm


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