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Measure and Integration

  • Textbook
  • © 2016

Overview

Authors:
  1. Hari Bercovici

    1. Department of Mathematics, Indiana University, Bloomington, USA

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  2. Arlen Brown

    1. Department of Mathematics, Indiana University, Bloomington, USA

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  3. Carl Pearcy

    1. Department of Mathematics, Texas A&M University, College Station, USA

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  • Axiomatic treatment of Lebesgue integration allows quick access to the main convergence of theorems

  • Includes a brief introduction to Fourier analysis in the Euclidean setting

  • Provides a treatment of standard measure spaces and analytic sets

  • Detailed index provides easy navigation to the main results

  • Includes supplementary material: sn.pub/extras

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xi
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  2. Rings of sets

    • Hari Bercovici, Arlen Brown, Carl Pearcy
    Pages 1-18

  3. Measurability

    • Hari Bercovici, Arlen Brown, Carl Pearcy
    Pages 19-42

  4. Integrals and measures

    • Hari Bercovici, Arlen Brown, Carl Pearcy
    Pages 43-73

  5. Convergence theorems for Lebesgue integrals

    • Hari Bercovici, Arlen Brown, Carl Pearcy
    Pages 75-104

  6. Existence and uniqueness of measures

    • Hari Bercovici, Arlen Brown, Carl Pearcy
    Pages 105-132

  7. Signed measures, complex measures, and absolute continuity

    • Hari Bercovici, Arlen Brown, Carl Pearcy
    Pages 133-165

  8. Measure and topology

    • Hari Bercovici, Arlen Brown, Carl Pearcy
    Pages 167-182

  9. Product measures

    • Hari Bercovici, Arlen Brown, Carl Pearcy
    Pages 183-201

  10. The L p spaces

    • Hari Bercovici, Arlen Brown, Carl Pearcy
    Pages 203-239

  11. Fourier analysis

    • Hari Bercovici, Arlen Brown, Carl Pearcy
    Pages 241-263

  12. Standard measure spaces

    • Hari Bercovici, Arlen Brown, Carl Pearcy
    Pages 265-284

  13. Back Matter

    Pages 285-300
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Keywords

About this book

This book covers the material of a one year course in real analysis.  It includes an original axiomatic approach to Lebesgue integration which the authors have found to be effective in the classroom.  Each chapter contains numerous examples and an extensive problem set which expands considerably the breadth of the material covered in the text.  Hints are included for some of the more difficult problems.                

Reviews

“The book is a perfect introduction for graduate students into the theory of measure and Lebesgue integration. It is written in a very pedagogical way providing in each chapter many examples and a long collection of problems with a number of hints for the more challenging ones.” (Oscar Blasco, zbMATH 1337.28001, 2016)

                   

Authors and Affiliations

  • Department of Mathematics, Indiana University, Bloomington, USA

    Hari Bercovici, Arlen Brown

  • Department of Mathematics, Texas A&M University, College Station, USA

    Carl Pearcy

About the authors

Hari Bercovici is a Professor in the Department of Mathematics at Indiana University Bloomington.  His research interests include functional analysis, operator theory, and free probability.

Carl Pearcy is an Emeritus Professor in Mathematics at Texas A&M University. His research interest is in functional analysis.                     

Bibliographic Information

  • Book Title: Measure and Integration

  • Authors: Hari Bercovici, Arlen Brown, Carl Pearcy

  • DOI: https://doi.org/10.1007/978-3-319-29046-1

  • Publisher: Springer Cham

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

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-29044-7Published: 04 April 2016

  • Softcover ISBN: 978-3-319-80480-4Published: 25 April 2018

  • eBook ISBN: 978-3-319-29046-1Published: 17 March 2016

  • Edition Number: 1

  • Number of Pages: XI, 300

  • Topics: Measure and Integration, Real Functions

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