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＜電子ブック＞
Measure, Integral, Derivative : A Course on Lebesgue's Theory / by Sergei Ovchinnikov
(Universitext. ISSN:21916675)

版	1st ed. 2013.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	2013
大きさ	X, 146 p. 16 illus : online resource
著者標目	*Ovchinnikov, Sergei author SpringerLink (Online service)
件　名	LCSH:Measure theory LCSH:Functions of real variables LCSH:Mathematical analysis FREE:Measure and Integration FREE:Real Functions FREE:Analysis
一般注記	1 Preliminaries -- 2 Lebesgue Measure -- 3  Lebesgue Integration -- 4 Differentiation and Integration -- A Measure and Integral over Unbounded Sets -- Index This classroom-tested text is intended for a one-semester course in Lebesgue’s theory.  With over 180 exercises, the text takes an elementary approach, making it easily accessible to both 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 σ-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 HTTP:URL=https://doi.org/10.1007/978-1-4614-7196-7

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