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Introduction to Measure Theory and Integration

  • Textbook
  • © 2011

Overview

Authors:
  1. Luigi Ambrosio

    1. Scuola Normale Superiore, Pisa, Italy

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  2. Giuseppe Prato

    1. Scuola Normale Superiore, Pisa, Italy

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  3. Andrea Mennucci

    1. Scuola Normale Superiore, Pisa, Italy

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  • Good choice of exercises, supplemented with solutions
  • Modern view point on measure theory and integration
  • Classical results and proofs

Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 10)

Part of the book sub series: Lecture Notes (Scuola Normale Superiore) (LNSNS)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Measure spaces

    • Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 1-22

  3. Integration

    • Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 23-43

  4. Spaces of integrable functions

    • Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 45-59

  5. Hilbert spaces

    • Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 61-72

  6. Fourier series

    • Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 73-82

  7. Operations on measures

    • Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 83-118

  8. The fundamental theorem of the integral calculus

    • Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 119-127

  9. Measurable transformations

    • Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci
    Pages 129-135

  10. Back Matter

    Pages 137-187
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Keywords

About this book

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.

Authors and Affiliations

  • Scuola Normale Superiore, Pisa, Italy

    Luigi Ambrosio, Giuseppe Prato, Andrea Mennucci

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