Introduction to Measure Theory and Integration

  • Luigi Ambrosio
  • Giuseppe Da Prato
  • Andrea Mennucci

Part of the Appunti/Lecture Notes book series (PSNS, volume 10)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 1-22
  3. Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 23-43
  4. Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 45-59
  5. Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 61-72
  6. Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 73-82
  7. Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 83-118
  8. Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 119-127
  9. Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 129-135
  10. Back Matter
    Pages 137-187

About this book

Introduction

This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 2000-2011. The goal of the course was to present, in a quick but rigorous way, the modern point of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourier series, calculus and real analysis. The text can also pave the way to more advanced courses in probability, stochastic processes or geometric measure theory. Prerequisites for the book are a basic knowledge of calculus in one and several variables, metric spaces and linear algebra. All results presented here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutions to the exercises are provided in the final part of the book.

Keywords

Fourier series calculus measure theory real analysis space theory

Authors and affiliations

  • Luigi Ambrosio
    • 1
  • Giuseppe Da Prato
    • 1
  • Andrea Mennucci
    • 1
  1. 1.Scuola Normale SuperiorePisaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-88-7642-386-4
  • Copyright Information Scuola Normale Superiore Pisa 2011
  • Publisher Name Edizioni della Normale
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-88-7642-385-7
  • Online ISBN 978-88-7642-386-4
  • About this book