Syllabus

Measure Theory and Probability, Math 8656, Fall 1998

PREREQUISITE KNOWLEDGE: Some important prerequisite topics are uniform convergence, continuity, sequences and series of numbers and functions, Riemann integral, the topology (open, closed, compact sets, etc.) of the real line, and calculation skill in elementary calculus. The change of variables theorems for multiple integrals, Riemann-Stieltjes integration (to be also treated briefly in 8656), and metric spaces (which will also be treated briefly in 8656) will be useful from time to time. No previous course in either probability or measure theory is required.

APPROXIMATE OUTLINE OF THE COURSE (references to the textbook)

• Chapter 1, Probability spaces
• Chapter 2, Random variables
• Chapter 3, Distribution functions
• Chapter 4, Expectations: Theory
• Chapter 5, Expectations: Applications
• Chapter 6, Calculating probabilities and measures
• Chapter 7, Measure theory: Existence and uniqueness
• Chapter 8, Integration theory
• Chapter 9, Stochastic independence

Five homeworks will be assigned and will form part of the final grade.

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