36752, 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. Sigmafields.  Lecture notes: Set 1  Natalia  
Feb 1, R  Measure. SigmaFiniteness. Continuity of measure. Uniqueness (pilamba theorem)  Lecture notes: Set 1  Riccardo 
Here is an example of a nonmeasurable set. From Billingsley, page 45. HW1 is out. Solutions to HW1. 
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  Theresa  
Feb 13, T  Integral. Fatou's Lemma and Monotone Convergence Theorem.  Lecture notes: Set 3  Shamindra  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  Yue  HW2 is out. Solutions to HW2. 
Feb 20, T  Product Measure.  Lecture notes: Set 4  Yifan  
Feb 22, R  Product Measure (cont'd). Lp spaces.  Lecture notes: Set 4, 5 and 6.  Heejong  
Feb 27, T  Lp spaces (cont'd) and Conditional Expectation.  Lecture notes: Set 5 and 6.  Matteo  
Mar 1, R  Conditional Expectation. Regular Conditional Probabilities.  Lecture notes: Set 6. 
Wanshan Billingsley's take on conditional probabilities. 
HW3 is out. Solutions to HW3. 
Mar 6, T  Regular Conditional Probabilities. Martingales.  Lecture notes: Set 6 and 7. 
Pratik 

Mar 8, T  Martingales. Stopping Times.  Lecture notes: Set 7.  
Mar 13, T  Spring Break.  
Mar 15, T  Spring Break.  
Mar 20, T  Optional Stopping Theorem. Convergence in Probability  Lecture notes: Set 7 and 8. 
Maria 

Mar 22, R  Convergence in Probability, in mean and almost surely  Lecture notes: Set 8 and 9. 
Trey 
HW4 is out. Solutions to HW4. 
Mar 27, T  Relationship between convergence in probability, law and almost surely. BorelCantelli Lemmas.  Lecture notes: Set 8 and 9. 
Riccardo 

Mar 29, R  SLLN and converence in distribution.  Lecture notes: Set 9 and 10. 
Natalia 

Apr 3, T  Convergence in distribution. Portmanteau and Continuous Mapping Theorem  Lecture notes: 10.  
Apr 5, R  Continuous Mapping Theorems, Slutsky Theorems.  Lecture notes: 10. 
Wanshan 
HW5 is out. Solutions to HW5. 
Apr 10, T  Op and op notation. Delta Method.  Lecture notes: 10.  
Apr 12, R  CLT.  Lecture notes: 11. 
Theresa 

Apr 17, T  Berry Esseen bound, CLT in high dimesnions.  Lecture notes: 11. 
Heejong 

Apr 19, R  No class (CMU Carnival).  
Apr 24, T  Efficient Lieklihood Estimation.  Chapter 4 of Jon Wellner's notes. 
Ron 

Apr 26, R  Efficient Lieklihood Estimation.  Chapter 4 of Jon Wellner's notes.  
May 1, T  Concentration of measure in high dimensions.  See references webpage for a list of sources on this topic. 
Yifan 

May 3, R  Concentration of measure in high dimensions.  See references webpage for a list of sources on this topic. 