A Course on Integration Theory - including more than 150 exercises with detailed answers (Paperback, 2014 ed.)

This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Caratheodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change of variables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality are proven. The Radon-Nikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems, including Marcinkiewicz's theorem, the definition of Lebesgue points and Lebesgue differentiation theorem are further topics included. A detailed appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. The appendix also provides more advanced material such as some basic properties of cardinals and ordinals which are useful in the study of measurability. "

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Release date:	March 2014
First published:	2014
Authors:	Nicolas Lerner
Dimensions:	235 x 155 x 27mm (L x W x T)
Format:	Paperback
Pages:	492
Edition:	2014 ed.
ISBN-13:	978-3-03-480693-0
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
LSN:	3-03-480693-0
Barcode:	9783034806930

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