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© 2015

Introduction to Measure Theory and Functional Analysis

Benefits

  • Highlights interaction between integration theory and functional analysis, with constant focus on applications

  • Includes a large number of examples and exercises, often proposed with hints for the reader

  • Self-contained exposition thanks to numerous reminders covered in the appendices

Textbook

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

  1. 1.Department of MathematicsUniversità degli Studi di Roma "Tor Vergata"RomaItaly
  2. 2.Department of MathematicsUniversità degli Studi di Roma "Tor Vergata"RomaItaly

About the authors

Prof. Piermarco Cannarsa, Full professor in Mathematical Analysis, Dept. of Mathematics, Università degli Studi di Roma "Tor Vergata", via della Ricerca Scientifica 1, 00133 Roma, Italy and Italian coordinator of the European Research Group (GDRE) on "Control of Partial Differential Equations" (CONEDP) issued by CNRS, INdAM and Universite' de Provence.

Prof. Teresa D'Aprile, Dept. of Mathematics, Università degli Studi di Roma "Tor Vergata", via della Ricerca Scientifica 1, 00133 Roma, Italy

Bibliographic information

Reviews

“This is an excellent introductory text on measure theory and integration, with a very good presentation of two fundamental aspects of functional analysis: Hilbert spaces and Banach spaces. The material is presented at a level accessible for a graduate student in mathematics or a researcher in another, related discipline. … Each section contains a large number of examples and exercises accompanied by generous hints.” (Victoria R. Steblovskaya, Mathematical Reviews, June, 2016)

“This book, written by leading experts, is a well-crafted textbook covering a medley of relevant topics in measure theory and functional analysis in a rather get-to-the-point-quickly fashion, yet resulting in a very readable and enjoyable journey. … The book manages to cover quite a lot of ground in a relatively short number of pages strewn with plenty of exercises. … All-in-all, the student reading this book stands to gain much knowledge, develop and hone her skills, and enjoy the trip.” (Ittay Weiss, MAA Reviews, maa.org, April, 2016)