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Birkhäuser

Measure and Integral

  • Textbook
  • © 2015

Overview

Authors:
  1. Martin Brokate

    1. TU München, Garching, Germany

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    You can also search for this author in PubMed   Google Scholar

  2. Götz Kersting

    1. Institut für Mathematik, Goethe-Universität Frankfurt, Frankfurt am Main, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • New arrangement of the subject matter with hands-on examples
  • Concise presentation of the material
  • Provides guidance and material for different variants of 2-hour courses
  • Focuses on the essentials of measure and integration theory
  • Includes supplementary material: sn.pub/extras

Part of the book series: Compact Textbooks in Mathematics (CTM)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. Introduction

    • Martin Brokate, Götz Kersting
    Pages 1-6

  3. Measurability

    • Martin Brokate, Götz Kersting
    Pages 7-17

  4. Measures

    • Martin Brokate, Götz Kersting
    Pages 19-27

  5. The Integral of Nonnegative Functions

    • Martin Brokate, Götz Kersting
    Pages 29-39

  6. Integrable Functions

    • Martin Brokate, Götz Kersting
    Pages 41-52

  7. Convergence

    • Martin Brokate, Götz Kersting
    Pages 53-62

  8. Uniqueness and Regularity of Measures

    • Martin Brokate, Götz Kersting
    Pages 63-71

  9. Multiple Integrals and Product Measures

    • Martin Brokate, Götz Kersting
    Pages 73-86

  10. Absolute Continuity

    • Martin Brokate, Götz Kersting
    Pages 87-107

  11. The Jacobi Transformation Formula

    • Martin Brokate, Götz Kersting
    Pages 109-115

  12. Construction of Measures

    • Martin Brokate, Götz Kersting
    Pages 117-135

  13. Hilbert Spaces

    • Martin Brokate, Götz Kersting
    Pages 137-152

  14. Banach Spaces

    • Martin Brokate, Götz Kersting
    Pages 153-167

  15. Back Matter

    Pages 169-172
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Keywords

About this book

The Lebesgue integral is an essential tool in the fields of analysis and stochastics and for this reason, in many areas where mathematics is applied. This textbook is a concise, lecture-tested introduction to measure and integration theory. It addresses the important topics of this theory and presents additional results which establish connections to other areas of mathematics. The arrangement of the material should allow the adoption of this textbook in differently composed Bachelor programmes.

Authors and Affiliations

  • TU München, Garching, Germany

    Martin Brokate

  • Institut für Mathematik, Goethe-Universität Frankfurt, Frankfurt am Main, Germany

    Götz Kersting

About the authors

Martin Brokate is Professor for Mathematical Modelling at TU Munich, Germany. Götz Kersting is Professor for Stochastics at the Goethe University in Frankfurt / Main, Germany.

Bibliographic Information

  • Book Title: Measure and Integral

  • Authors: Martin Brokate, Götz Kersting

  • Series Title: Compact Textbooks in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-15365-0

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Softcover ISBN: 978-3-319-15364-3Published: 09 July 2015

  • eBook ISBN: 978-3-319-15365-0Published: 24 June 2015

  • Series ISSN: 2296-4568

  • Series E-ISSN: 2296-455X

  • Edition Number: 1

  • Number of Pages: VII, 172

  • Number of Illustrations: 24 b/w illustrations

  • Topics: Measure and Integration

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