Authors:
- Contains all the main results of Lebesgue’s theory
- Accessible to both upper-undergraduate and master’s students
- Includes 180+ exercises with varying degrees of difficulty
- Request lecturer material: sn.pub/lecturer-material
Part of the book series: Universitext (UTX)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
About this book
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
Reviews
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 Cárdenas-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)
Authors and Affiliations
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Dept. Mathematics, San Francisco State University, San Francisco, USA
Sergei Ovchinnikov
About the author
Bibliographic Information
Book Title: Measure, Integral, Derivative
Book Subtitle: A Course on Lebesgue's Theory
Authors: Sergei Ovchinnikov
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4614-7196-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Softcover ISBN: 978-1-4614-7195-0Published: 30 April 2013
eBook ISBN: 978-1-4614-7196-7Published: 08 July 2014
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: X, 146
Number of Illustrations: 16 b/w illustrations
Topics: Measure and Integration, Real Functions, Analysis