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  • Textbook
  • © 2015

Measure and Integral

Birkhäuser
  • 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
  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

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

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access