Measure, Integral, Derivative: A Course on Lebesgue's Theory (Universitext) - Softcover

Ovchinnikov, Sergei

Softcover

ISBN 10: 1461471958 ISBN 13: 9781461471950

Publisher: Springer, 2013

Synopsis

Featuring over 180 exercises, this text for a one-semester course in Lebesgue’s theory takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students.

About this title

About the Author

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

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2013
• Language: English
• ISBN 10: 1461471958
• ISBN 13: 9781461471950
• Binding: Paperback
• Number of pages: 156