Measure, Integral, Derivative

A Course on Lebesgue's Theory

  • Sergei Ovchinnikov

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-X
  2. Sergei Ovchinnikov
    Pages 1-26
  3. Sergei Ovchinnikov
    Pages 27-64
  4. Sergei Ovchinnikov
    Pages 65-95
  5. Sergei Ovchinnikov
    Pages 97-127
  6. Back Matter
    Pages 129-146

About this book

Introduction

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.

Keywords

Lebesgue integration Lebesgue measure analysis differentiability of BV-functions measurable sets

Authors and affiliations

  • Sergei Ovchinnikov
    • 1
  1. 1.Dept. MathematicsSan Francisco State UniversitySan FranciscoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-7196-7
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-7195-0
  • Online ISBN 978-1-4614-7196-7
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
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