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Book Cover
E-book
Author Ovchinnikov, Sergeĭ.

Title Measure, integral, derivative : a course on Lebesgue's theory / Sergei Ovchinnikov
Published New York, NY : Springer, ©2013

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Description 1 online resource
Series Universitext, 0172-5939
Universitext.
Contents Preliminaries -- Lebesgue Measure -- Lebesgue Integration -- Differentiation and Integration
Summary This classroom-tested text is intended for a one-semester course in Lebesgue's theory. With over 180 exercises, the texttakes an elementary approach, making iteasily accessible toboth upper-undergraduate- and lower-graduate-level students. The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text. The presentation is elementary, where [sigma]-algebras are not used in the text on measure theory and Dini's derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgue's theory are found in the book
Analysis Mathematics
Global analysis (Mathematics)
Measure and Integration
Real Functions
Analysis
Bibliography Includes bibliographical references and index
Subject Lebesgue integral.
Integración funcional
Lebesgue integral
Maßtheorie
Integrationstheorie
Lebesgue-Maß
Lebesgue-Integral
Form Electronic book
ISBN 9781461471967
1461471966
1461471958
9781461471950