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A Concise Introduction to Measure Theory

  • Satish Shirali

Table of contents

  1. Front Matter
    Pages i-x
  2. Satish Shirali
    Pages 1-18
  3. Satish Shirali
    Pages 19-37
  4. Satish Shirali
    Pages 39-63
  5. Satish Shirali
    Pages 65-89
  6. Satish Shirali
    Pages 91-102
  7. Satish Shirali
    Pages 103-126
  8. Satish Shirali
    Pages 127-167
  9. Satish Shirali
    Pages 169-178
  10. Back Matter
    Pages 179-271

About this book

Introduction

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.

Keywords

Measure and integration Lebesgue measure Fubini and Tonelli theorems Fundamental theorem of calculus Cantor set Lebesgue differentiability theorem Absolute continuity Vitali covering theorem Fuzzy measure Product measure Outer measure

Authors and affiliations

  • Satish Shirali
    • 1
  1. 1.Formerly of Panjab UniversityChandigarhIndia

Bibliographic information