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Catalogue Information
Field name	Details
Dewey Class	515.42
Title	Measure, Integral, Derivative (EB) : A Course on Lebesgue's Theory / by Sergei Ovchinnikov.
Author	Ovchinnikov, Sergei
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer
Publication	, 2013.
Physical Details	X, 146 pages, 16 illus. : online resource.
Series	Universitext 0172-5939
ISBN	9781461471967
Summary Note	This classroom-tested text is intended for a one-semester course in Lebesgueâs 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 Ï-algebras are not used in the text on measure theory and Diniâs derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgueâs theory are found in the book.:
Contents note	1 Preliminaries -- 2 Lebesgue Measure -- 3Â Lebesgue Integration -- 4 Differentiation and Integration -- A Measure and Integral over Unbounded Sets -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4614-7196-7
Links to Related Works	Subject References: Analysis . Functions of real variables . Global analysis (Mathematics) . Lebesgue integral . Measure and Integration . Measure theory . Real Functions . Authors: Ovchinnikov, Sergei . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 515.42 . 515.42 (DDC 23) .

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Measure, Integral, Derivative: A Course on Lebesgue's Theory

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