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A Concise Introduction to Measure Theory

  • Textbook
  • © 2018

Overview

Authors:
  1. Satish Shirali

    1. Formerly of Panjab University, Chandigarh, India

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  • Provides a self-contained introduction to abstract measure theory and integration

  • Includes full solutions to the exercises

  • Discusses fuzzy measures and unconditional sums

  • 19k Accesses

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-x
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  2. Preliminaries

    • Satish Shirali
    Pages 1-18

  3. Measure Space and Integral

    • Satish Shirali
    Pages 19-37

  4. Properties of the Integral

    • Satish Shirali
    Pages 39-63

  5. Construction of a Measure

    • Satish Shirali
    Pages 65-89

  6. The Counting Measure

    • Satish Shirali
    Pages 91-102

  7. Product Measures

    • Satish Shirali
    Pages 103-126

  8. Differentiation

    • Satish Shirali
    Pages 127-167

  9. The Cantor Set and Function

    • Satish Shirali
    Pages 169-178

  10. Back Matter

    Pages 179-271
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Keywords

About this book

This undergraduate textbook offers a self-contained and concise introduction to measure theory and integration.


The author takes an approach to integration based on the notion of distribution. This approach relies on deeper properties of the Riemann integral which may not be covered in standard undergraduate courses. It has certain advantages, notably simplifying the extension to "fuzzy" measures, which is one of the many topics covered in the book.


This book will be accessible to undergraduate students who have completed a first course in the foundations of analysis. Containing numerous examples as well as fully solved exercises, it is exceptionally well suited for self-study or as a supplement to lecture courses.

Authors and Affiliations

  • Formerly of Panjab University, Chandigarh, India

    Satish Shirali

About the author

Satish Shirali's research interests have been in Banach *-algebras, elliptic boundary value problems, and fuzzy measures. He is the co-author of three books: Introduction to Mathematical Analysis (2014), Multivariable Analysis (2011) and Metric Spaces (2006), the latter two published by Springer.

Bibliographic Information

  • Book Title: A Concise Introduction to Measure Theory

  • Authors: Satish Shirali

  • DOI: https://doi.org/10.1007/978-3-030-03241-8

  • Publisher: Springer Cham

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

  • Copyright Information: Springer Nature Switzerland AG 2018

  • Softcover ISBN: 978-3-030-03240-1Published: 15 March 2019

  • eBook ISBN: 978-3-030-03241-8Published: 27 February 2019

  • Edition Number: 1

  • Number of Pages: X, 271

  • Number of Illustrations: 16 b/w illustrations, 1 illustrations in colour

  • Topics: Measure and Integration, Calculus, Real Functions

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