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

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Book Description

Now considered a classic version on the topic; Measure and Integral: An Introduction to Real Analysis; 2^nd Edition; (PDF) offers an introduction to real analysis by first forming the theory of measure and integration in the simple setting of Euclidean space; and then offering a more general treatment based on abstract notions categorized by axioms and with less geometric content.

Published almost forty years after the first edition; this long-awaited Second Edition also:

• • Analyzes the Fourier transform of functions in the spaces L¹; L²; and L^p; 1 < p < 2

• • Demonstrates the existence of a tangent plane to the graph of a Lipschitz function of several variables

• • Lengthens the subrepresentation formula derived for smooth functions to functions with a weak gradient

• • Displays 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

• • Uses the norm estimates derived for fractional integral operators to get local and global first-order Poincaré–Sobolev inequalities; including endpoint cases

• • Develops a subrepresentation formula; which in higher dimensions plays a role quite similar to the one played by the fundamental theorem of calculus in one dimension

• • Includes fractional integration and some topics related to mean oscillation properties of functions; like the classes of Hölder continuous functions and the space of functions of bounded mean oscillation

Contains many new exercises not present in the first edition

This highly respected and extensively used textbook Measure and Integral: An Introduction to Real Analysis 2e for upper-division undergraduate and first-year graduate students of mathematics; probability; statistics; or engineering is updated for a new generation of college students and instructors. The ebook also serves as a handy reference for professional mathematicians.

NOTE: The product only includes the ebook; Measure and Integral: An Introduction to Real Analysis; 2nd Edition in PDF. No access codes are included.