1. Measure theory; 2. Laws of large numbers; 3. Central limit theorems; 4. Martingales; 5. Markov chains; 6. Ergodic theorems; 7. Brownian motion; 8. Applications to random walk; 9. Multidimensional Brownian motion; Appendix. Measure theory details.
A well-written and lively introduction to measure theoretic probability for graduate students and researchers.
Rick Durrett is a James B. Duke professor in the mathematics department of Duke University, North Carolina. He received his Ph.D. in Operations Research from Stanford University in 1976. After nine years at University of California, Los Angeles and twenty-five at Cornell University, he moved to Duke University in 2010. He is the author of 8 books and more than 220 journal articles on a wide variety of topics, and has supervised more than 45 Ph.D. students. He is a member of National Academy of Science, American Academy of Arts and Sciences, and a fellow of the Institute of Mathematical Statistics, and of the American Mathematical Society.