Tentative Schedule

Ch.1 Distribution function
   
    1.1 Monotone functions

    1.2 Distribution functions

    1.3 Absolutely continuous and singular distributions

Ch.2 Measure theory
   
    2.1 Classes of sets

    2.2 Probability measures and their distribution functions

Ch3. Random variables, expectation, independence
   
    3.1 General definitions

    3.2 Properties of mathematical expectation

    Quiz 1, Oct. 12

    3.3 Independence

Ch4. Convergence concepts
   
    4.1 Various modes of convergence

    4.2 Almost sure convergence; Borel-Cantelli lemma

    4.3 Vague convergence

    Quiz 2, Nov. 16

    4.4 Continuation

    4.5 Uniform integrability: convergence of moments

      Final exam, Dec. 7, 7:00-9:00pm