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Measure and Integration

  • Textbook
  • © 2019

Overview

Authors:
  1. Satish Shirali

    1. Formerly of Panjab University, Chandigarh, India

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    You can also search for this author in PubMed   Google Scholar

  2. Harkrishan Lal Vasudeva

    1. Formerly of Panjab University, Chandigarh, India

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Supplements the abstract theory with a great amount of motivation, explanations and concrete examples
  • Includes background on metric spaces and mathematical analysis
  • Over 300 exercises with hints

Part of the book series: Springer Undergraduate Mathematics Series (SUMS)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
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  2. Preliminaries

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 1-42

  3. Measure in Euclidean Space

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 43-108

  4. Measure Spaces and Integration

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 109-162

  5. Fourier Series

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 163-209

  6. Differentiation

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 211-336

  7. Lebesgue Spaces and Modes of Convergence

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 337-374

  8. Product Measure and Completion

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 375-404

  9. Hints

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 405-590

  10. Back Matter

    Pages 591-598
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Keywords

About this book

This textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis.


Proceeding at a leisurely, student-friendly pace, the authors begin by recalling elementary notions of real analysis before proceeding to measure theory and Lebesgue integration. Further chapters cover Fourier series, differentiation, modes of convergence, and product measures. Noteworthy topics discussed in the text include Lp spaces, the Radon–Nikodým Theorem, signed measures, the Riesz Representation Theorem, and the Tonelli and Fubini Theorems.


This textbook, based on extensive teaching experience, is written for senior undergraduate and beginning graduate students in mathematics. With each topic carefully motivated and hints to more than 300 exercises, it is the ideal companion for self-study or use alongside lecture courses.

Authors and Affiliations

  • Formerly of Panjab University, Chandigarh, India

    Satish Shirali, Harkrishan Lal Vasudeva

About the authors

​Satish Shirali's research interest are in Banach *algebras, elliptic boundary value problems, fuzzy measures, and Harkrishan Vasudeva's interests are in functional analysis. This is their fourth joint textbook, having previous published An Introduction to Mathematical Analysis (2014), Multivariable Analysis (2011) and Metric Spaces (2006). Shirali is also the author of the book A Concise Introduction to Measure Theory (2018), and Vasudeva is the author of Elements of Hilbert Spaces and Operator Theory (2017) and co-author of An Introduction to Complex Analysis (2005).



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