OBJECTIVE: After taking this course, the students would have a solid knowledge of the foundations for probability theory, in terms of the real analysis perspective.

References
1. Billingsley, Patrick, 1995, Probability and Measure, 3rd ed., John Wiley &Sons.
2. Aliprantis, Charalambos D. and Owen Burkinshaw, 1998, Principles of Real Analysis, 3rd ed., Academic Press.
3. Royden, H. L., 1988, Real Analysis, 3rd ed., Prentice-Hall.
4. Karlin, Samuel and Howard M. Taylor, 1975, A First Course in Stochastic Processes, 2nd ed., Academic Press.

TOPICS (subject to revision): Metric Spaces, Topological Spaces, Normed Vector Spaces and Lp Spaces, General Measures, Lebesgue Measure, Measurable Sets, Measurable Functions, Distribution Functions, Random Variables and Distributions, Integrable Functions, Lebesgue Integral, Expected Values, Fubini’s Theorem, Radon-Nikodym Theorem, Markov Chains, Poisson Processes, Martingales (if time allows).

GRADING: Homework and Presentations: 30%. Mid-Term Exam: 35%. Final Exam: 35%.