MEASURE THEORY AND PROBABILITY--------PHI
Description:
This compact and well-received 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 first-year 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).
Contents:
List of Symbols and Abbreviations
1. Introduction: Sets, Indicator Functions, and Classes of Sets
2. Measure Space and Probability Space
3. 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 Lebesgue-Stieltjes Measure
Appendix I Measure on Infinite Product Space and Kolmogorov’s Consistency
Appendix II Hahn-Jordan Decomposition
Appendix III Large Sample Theory
References • Author Index • Subject Index
