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Introduction to Measure Theory and Functional Analysis

  • Piermarco Cannarsa
  • Teresa D'Aprile

Part of the UNITEXT book series (UNITEXT, volume 89)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT, volume 89)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Measure and Integration

    1. Front Matter
      Pages 1-1
    2. Piermarco Cannarsa, Teresa D’Aprile
      Pages 3-35
    3. Piermarco Cannarsa, Teresa D’Aprile
      Pages 37-80
    4. Piermarco Cannarsa, Teresa D’Aprile
      Pages 81-106
    5. Piermarco Cannarsa, Teresa D’Aprile
      Pages 107-130
  3. Functional Analysis

    1. Front Matter
      Pages 131-131
    2. Piermarco Cannarsa, Teresa D’Aprile
      Pages 133-166
    3. Piermarco Cannarsa, Teresa D’Aprile
      Pages 167-225
  4. Selected Topics

    1. Front Matter
      Pages 227-227
    2. Piermarco Cannarsa, Teresa D’Aprile
      Pages 229-252
    3. Piermarco Cannarsa, Teresa D’Aprile
      Pages 253-270
    4. Piermarco Cannarsa, Teresa D’Aprile
      Pages 271-277
  5. Back Matter
    Pages 279-314

About this book

Introduction

This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two courses, it can be supplemented by additional topics from the third part of the book, such as functions of bounded variation, absolutely continuous functions, and signed measures.

This textbook addresses the needs of graduate students in mathematics, who will find the basic material they will need in their future careers, as well as those of researchers, who will appreciate the self-contained exposition which requires no other preliminaries than basic calculus and linear algebra.

Keywords

Functional analysis Functions of bounded variations Integration Measure theory Set-valued maps

Authors and affiliations

  • Piermarco Cannarsa
    • 1
  • Teresa D'Aprile
    • 2
  1. 1.Department of MathematicsUniversità degli Studi di Roma "Tor Vergata"RomaItaly
  2. 2.Department of MathematicsUniversità degli Studi di Roma "Tor Vergata"RomaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-17019-0
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-17018-3
  • Online ISBN 978-3-319-17019-0
  • Series Print ISSN 2038-5714
  • Buy this book on publisher's site
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