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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis
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Measure and Integral - An Introduction to Real Analysis, Second Edition (Hardcover, 2nd edition)
Loot Price: R3,416
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Measure and Integral - An Introduction to Real Analysis, Second Edition (Hardcover, 2nd edition)
Series: Chapman & Hall/CRC Pure and Applied Mathematics
Expected to ship within 9 - 15 working days
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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 < 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 Hoelder 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 Poincare-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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