Elements of Measure and Probability

Contents: Preface. 1. Preliminaries. 2. Classes of sets. 3. Introduction to measures. 4. Extension of measures. 5. Lebesgue-Stieltjes measures. 6. Measurable functions. 7. Integral. 8. Basic inequalities. 9. Lp spaces: topological properties. 10. Product spaces and transition measures. 11. Random variables and vectors. 12. Moments and cumulants. 13. Further modes of convergence of functions. 14. Independence and basic conditional probability. 15. 0 − 1 laws. 16. Sums of independent random variables. 17. Convergence of finite measures. 18. Characteristic function. 19. Central limit theorem. 20. Signed measure. 21. Radon-Nikodym theorem. 22. Fundamental theorem of calculus. 23. Conditional expectation. Bibliography. Author Index. Subject Index.

This is an introduction to Measure Theory and Measure Theoretic Probability at the upper undergraduate and graduate levels. A familiarity with real analysis is required. Some background in basic probability would be helpful,  but is not essential.

The book can be used for courses in both mathematics and mathematical statistics. All the standard topics in measure theory and probability are covered. A large number of exercises are provided throughout the book.