Measure Theory And Probability

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.

This book Useful for postgraduate & engineering students.

1. Measure theory and probability are well integrated.

2. Exercises are given at the end of each chapter, with solutions provided separately.

3. A section is devoted to large sample theory of statistics, and another to large deviation theory (in the Appendix).

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

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