Lecture notes updated (please read)

I have updated the lecture notes. Things to note:

1) You have some solutions for Chapter 5. Try to solve the exercises from Chapter 5 if you have not done so, before checking the solutions.

2) Now you have everything until Chapter 6 (included). You can start trying to solve the exercises of Chapter 6 (Exercise 6.4 was solved on the blackboard yesterday).

3) I have rewritten the proof of the equivalent definition of almost sure convergence. It is the same as yesterday, but more rigorous and justifying measurability inside the probability. Also, please check the proofs of: Proposition 6.3.1 and Proposition 6.4.1.

4) Next week we will start Chapter 7 on conditional expectation and Wednesday will be devoted to solving more exercises from Chapter 5 and 6.