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Book Summary of Measure Theory And Probability
This compact and wellreceived book, now in its second edition, is a skilful combination of measure theory and probability. For, in contrast to many books where probability theory is usually developed after a thorough exposure to the theory and techniques of measure and integration, this text develops the Lebesgue theory of measure and integration, using probability theory as the motivating force.
What distinguishes the text is the illustration of all theorems by examples and applications. A section on Stieltjes integration assists the student in understanding the later text better.
For easy understanding and presentation, this edition has split some long chapters into smaller ones. For example, old Chapter 3 has been split into Chapters 3 and 9, and old Chapter 11 has been split into Chapters 11, 12 and 13.
The book is intended for the firstyear postgraduate students for their courses in Statistics and Mathematics (pure and applied), computer science, and electrical and industrial engineering.
KEY FEATURES :
Measure theory and probability are well integrated.
Exercises are given at the end of each chapter, with solutions provided separately.
A section is devoted to large sample theory of statistics, and another to large deviation theory (in the Appendix).
About the Author
(Late) A.K. BASU, PhD, was formerly faculty in the Department of Statistics, Calcutta University. His various assignments saw him serving at the University of Illinois (Chicago), University of Brasilia (Brazil), and the Laurentian University (Canada). Besides, he was a Visiting Faculty at the University of Regina, McMaster, and Ottawa (all in Canada); IPN (Mexico); and the Indian Statistical Institute, Calcutta.
About the Author
(Late) A.K. BASU, PhD, was formerly faculty in the Department of Statistics, Calcutta University. His various assignments saw him serving at the University of Illinois (Chicago), University of Brasilia (Brazil), and the Laurentian University (Canada). Besides, he was a Visiting Faculty at the University of Regina, McMaster, and Ottawa (all in Canada); IPN (Mexico); and the Indian Statistical Institute, Calcutta.
Dr. Basu was a member of the Institute of Mathematical Statistics, International Statistical Association, and the Statistical Science Association of Canada. He published several articles in reputed national and international journals.
Table of Contents
Editor’s Preface Preface to the First Edition List of Symbols and Abbreviations
1. Introduction: Sets, Indicator Functions, and Classes of Sets
2. Measure Space and Probability Space
Distribution Functions
4. Measurable Functions
5. Integration Theory and Expectation
6. Types of Convergence and Limit Theorems
7. Independence
8. Law of Large Numbers and Associated Limit Theorems
9. Characteristic Functions
10. Central Limit Theorem (CLT)
11. Product Space
12. Conditional Expectation
13. Martingale
14. Measure Extension and LebesgueStieltjes Measure
Appendix I Measure on Infinite Product Space and Kolmogorov’s Consistency
Appendix II HahnJordan Decomposition
Appendix III Large Sample Theory References
Author Index
Subject Index
Table of Contents
Editor’s Preface Preface to the First Edition List of Symbols and Abbreviations
1. Introduction: Sets, Indicator Functions, and Classes of Sets
2. Measure Space and Probability Space
Distribution Functions
4. Measurable Functions
5. Integration Theory and Expectation
6. Types of Convergence and Limit Theorems
7. Independence
8. Law of Large Numbers and Associated Limit Theorems
9. Characteristic Functions
10. Central Limit Theorem (CLT)
11. Product Space
12. Conditional Expectation
13. Martingale
14. Measure Extension and LebesgueStieltjes Measure
Appendix I Measure on Infinite Product Space and Kolmogorov’s Consistency
Appendix II HahnJordan Decomposition
Appendix III Large Sample Theory References
Author Index
Subject Index
Details of Book: Measure Theory And Probability
| Book: | Measure Theory And Probability |
| Author: | A. K. Basu |
| ISBN: | 8120343859 |
| ISBN-13: | 9788120343856,978-8120343856 |
| Publishing Date: | 2012 |
| Publisher: | PHI LEARNING PVT. LTD-NEW DELHI |
| Edition: | 2ndEdition |
| Number of Pages: | 240 |
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