STAT 571
Probability and Measure
Winter 2020 · Measure Theory for Probability
Topics
- Measure and integration
- Random variables and distributions
- Product measures and Fubini theorem
- Independence and consistency
- Laws of large numbers
- Borel–Cantelli lemmas
- Weak convergence
- Characteristic functions
- Central limit theorems
- Conditional expectation
Readings
- Billingsley. Probability and Measure.
- Rosenthal. A First Look at Rigorous Probability Theory.
- Durrett. Probability, Theory and Examples.