Measure, Integral, Derivative

A Course on Lebesgue's Theory

AvSergei Ovchinnikov

Häftad, Engelska, 2013

Del i serien Universitext

694 kr

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Beskrivning

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://online.sfsu.edu/sergei/MID.htm

Produktinformation

Utgivningsdatum:2013-04-30
Mått:155 x 235 x 9 mm
Vikt:248 g
Format:Häftad
Språk:Engelska
Serie:Universitext
Antal sidor:146
Upplaga:2013
Förlag:Springer-Verlag New York Inc.
ISBN:9781461471950

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Sergei Ovchinnikov is currently Professor of Mathematics at San Francisco State University.

Recensioner i media

From the reviews: "It is accessible to upper-undergraduate and lower graduate level students, and the only prerequisite is a course in elementary real analysis. ... The book proposes 187 exercises where almost always the reader is proposed to prove a statement. ... this book is a very helpful tool to get into Lebesgue's theory in an easy manner." (Daniel Cardenas-Morales, zbMATH, Vol. 1277, 2014) "This is a brief ... but enjoyable book on Lebesgue measure and Lebesgue integration at the advanced undergraduate level. ... The presentation is clear, and detailed proofs of all results are given. ... The book is certainly well suited for a one-semester undergraduate course in Lebesgue measure and Lebesgue integration. In addition, the long list of exercises provides the instructor with a useful collection of homework problems. Alternatively, the book could be used for self-study by the serious undergraduate student." (Lars Olsen, Mathematical Reviews, December, 2013)

Innehållsförteckning

1 Preliminaries.- 2 Lebesgue Measure.- 3 Lebesgue Integration.- 4 Differentiation and Integration.- A Measure and Integral over Unbounded Sets.- Index.