36-752, Spring 2018
Class Schedule
Date Lecture Topic Readings Scribe Notes Notes
Jan 16, T No class
Jan 18, R No class
Jan 23, T No class
Jan 25, R No class
Jan 30, T Course overview. Basic Set Theoretic Concepts. Sigma-fields. Lecture notes: Set 1 Natalia
Feb 1, R Measure. Sigma-Finiteness. Continuity of measure. Uniqueness (pi-lamba theorem) Lecture notes: Set 1 Riccardo Here is an example of a non-measurable set. From Billingsley, page 45.
HW1 is out.
Feb 6, T Carathedory extension thorem. Measures from distribution functions. Measurable functions and random variables. Lecture notes: Set 2 Ron
Feb 8, R Measurable functions and random variables. Integration. Lecture notes: Set 3
Feb 13, T Integral. Fatou's Lemma and Monotone Convergence Theorem. Lecture notes: Set 3 To compare the Lebesgue vs Riemann integral, see, e.g., this excerpt from the book "Mathematical Analysis", by Apostol, Addison Wesley (1981)
Feb 15, R Dominated convergence theorem. Densities. Product Measure. Lecture notes: Set 3 and 4 HW2 is out.

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