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AMS 569, Probability Theory I
Probability spaces and sigma-algebras. Random variables as measurable mappings. Borel-Cantelli lemmas. Expectation using simple functions. Monotone and dominated convergence theorems. Inequalities. Stochastic convergence. Characteristic functions. Laws of large numbers and the central limit theorem. 
PrerequisiteAMS 510
3 credits, ABCF grading 

Spring Semester

Required Textbook:
"Probability Essentials" by Jean Jacod and Philip Protter; 2nd edition (corrected second printing 2004); Springer;
ISBN: 978-3-642-55682-1 (eBook)