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Birkhäuser

Lebesgue Integral

  • Textbook
  • © 2021

Overview

Authors:
  1. Liviu C. Florescu

    1. Faculty of Mathematics, “Al. I. Cuza” University, Iaşi, Romania

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  • Provides an approach to the theory starting from real numbers
  • Includes original exercises that highlight interesting aspects of the theory
  • Presents elegant proofs

Part of the book series: Compact Textbooks in Mathematics (CTM)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xi
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  2. Lebesgue Measure on \(\mathbb R\)

    • Liviu C. Florescu
    Pages 1-30

  3. Measurable Functions

    • Liviu C. Florescu
    Pages 31-57

  4. Lebesgue Integral

    • Liviu C. Florescu
    Pages 59-96

  5. The L p Spaces

    • Liviu C. Florescu
    Pages 97-126

  6. Lebesgue Integral on \(\mathbb R^2\)

    • Liviu C. Florescu
    Pages 127-155

  7. Signed Measures

    • Liviu C. Florescu
    Pages 157-190

  8. Appendices

    • Liviu C. Florescu
    Pages 191-208

  9. Back Matter

    Pages 209-215
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Keywords

About this book

This book presents a compact and self-contained introduction to the theory of measure and integration. The introduction into this theory is as necessary (because of its multiple applications) as difficult for the uninitiated. Most measure theory treaties involve a large amount of prerequisites and present crucial theoretical challenges. By taking on another approach, this textbook provides less experienced readers with material that allows an easy access to the definition and main properties of the Lebesgue integral.

The book will be welcomed by upper undergraduate/early graduate students who wish to better understand certain concepts and results of probability theory, statistics, economic equilibrium theory, game theory, etc., where the Lebesgue integral makes its presence felt throughout. The book can also be useful to students in the faculties of mathematics, physics, computer science, engineering, life sciences, as an introduction to a more in-depth study of measure theory.


Authors and Affiliations

  • Faculty of Mathematics, “Al. I. Cuza” University, Iaşi, Romania

    Liviu C. Florescu

About the author

Liviu C. Florescu is Professor Emeritus at University "Al.I.Cuza" Iasi, Romania.

Bibliographic Information

  • Book Title: Lebesgue Integral

  • Authors: Liviu C. Florescu

  • Series Title: Compact Textbooks in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-60163-8

  • Publisher: Birkhäuser Cham

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

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Softcover ISBN: 978-3-030-60162-1Published: 26 February 2021

  • eBook ISBN: 978-3-030-60163-8Published: 25 February 2021

  • Series ISSN: 2296-4568

  • Series E-ISSN: 2296-455X

  • Edition Number: 1

  • Number of Pages: XI, 215

  • Number of Illustrations: 8 b/w illustrations, 1 illustrations in colour

  • Topics: Real Functions

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