Statistics 381: Measure-Theoretic Probability 1
Winter 2019
Instructor: Professor Steve Lalley
Office: 323 Jones Hall
Office Hour: Thursday 1:30 - 2:30
Phone: 702-9890
E-mail:
lalley@galton.uchicago.edu
Course Assistant: Changji Xu
Office Hour: TBA
This course is the first of a three-quarter sequence in
measure-theoretic probability. It is meant for students with a solid
grounding in real analysis. The main topics to be covered (not necessarily in the
order listed)
will be :
- Existence and Extensions of Measures (1 week)
- Independence; Borel's SLLN (1 week)
- Measurable Functions, Transformations, and Random Variables (1 week)
- Integration and Expectation (1-2 weeks)
- Sums of Independent Random Variables (2 weeks)
- Birkhoff's Ergodic Theorem(1 week)
- Weak Convergence (1 week)
- Fourier Analysis (1 week)
There will be weekly homework, a midterm and a final exam. Detailed
lecture notes will be posted as the course progresses.
Recommended Reading:
-
Probability and Measure by Patrick Billingsley
- Probability: Theory and Examples by Richard Durrett
Web pages from previous years:
Announcement:
The midterm exam will held on Friday, February 8 at the regular
class time. You may bring 1 page of notes.
Problem Sets:
Lecture Notes: