Probability with Martingales

1. A branching-process example Part I. Foundations: 2. Measure spaces 3. Events 4. Random variables 5. Independence 6. Integration 7. Expectation 8. An easy strong law: product measure Part II. Martingale Theory: 9. Conditional expectation 10. Martingales 11. The convergence theorem 12. Martingales bounded in L2 13. Uniform integrability 14. UI martingales 15. Applications Part III. Characteristic Functions: 16. Basic properties of CFs 17. Weak convergence 18. The central limit theorem Appendices Exercises.