Measure, Integral, Derivative

A Course on Lebesgue's Theory

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Calculus
Cover of the book Measure, Integral, Derivative by Sergei Ovchinnikov, Springer New York
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Author: Sergei Ovchinnikov ISBN: 9781461471967
Publisher: Springer New York Publication: July 8, 2014
Imprint: Springer Language: English
Author: Sergei Ovchinnikov
ISBN: 9781461471967
Publisher: Springer New York
Publication: July 8, 2014
Imprint: Springer
Language: English

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

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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

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