Measure theory and Integration ( 2 )

Publication series :2

Author: Barra   G De  

Publisher: Elsevier Science‎

Publication year: 2003

E-ISBN: 9780857099525

P-ISBN(Paperback): 9781904275046

P-ISBN(Hardback):  9781904275046

Subject: O174.12 (signed)

Language: ENG

Access to resources Favorite

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Description

This text approaches integration via measure theory as opposed to measure theory via integration, an approach which makes it easier to grasp the subject. Apart from its central importance to pure mathematics, the material is also relevant to applied mathematics and probability, with proof of the mathematics set out clearly and in considerable detail. Numerous worked examples necessary for teaching and learning at undergraduate level constitute a strong feature of the book, and after studying statements of results of the theorems, students should be able to attempt the 300 problem exercises which test comprehension and for which detailed solutions are provided.

  • Approaches integration via measure theory, as opposed to measure theory via integration, making it easier to understand the subject
  • Includes numerous worked examples necessary for teaching and learning at undergraduate level
  • Detailed solutions are provided for the 300 problem exercises which test comprehension of the theorems provided

Chapter

Front Cover

pp.:  1 – 4

ABOUT OUR AUTHOR

pp.:  3 – 10

Copyright Page

pp.:  5 – 6

Table of Contents

pp.:  6 – 3

Preface to First Edition

pp.:  10 – 12

Notation

pp.:  12 – 16

Chapter 1. Preliminaries

pp.:  16 – 28

Chapter 2. Measure on the Real Line

pp.:  28 – 55

Chapter 3. Integration of Functions of a Real Variable

pp.:  55 – 78

Chapter 4. Differentiation

pp.:  78 – 94

Chapter 5. Abstract Measure Spaces

pp.:  94 – 110

Chapter 6. Inequalities and the Lp Spaces

pp.:  110 – 122

Chapter 7. Convergence

pp.:  122 – 134

Chapter 8. Signed Measures and their Derivatives

pp.:  134 – 154

Chapter 9. Lebesgue-Stieltjes Integration

pp.:  154 – 177

Chapter 10. Measure and Integration in a Product Space

pp.:  177 – 198

Hints and Answers to Exercises

pp.:  198 – 237

References

pp.:  237 – 238

Index

pp.:  238 – 241

The users who browse this book also browse