### 4.2. Martingales and a.s. convergence

probability Durrett

Remaining sections in chapter 4 is about martingales and convergence of it. Regarding martingales, our first topic will be convergence in almost sure sense. Next we will look into convergence in $L^p,$ with $p>1$ and $p=1$ separately. In the meantime the theory of optional stopping will be covered.

### 4.1. Conditional expectation

probability Durrett

In this chapter we study convergence of a sequence of random variables with dependency. To be specific, I will cover theory of martingales. The first subsection is about conditional expectation which is essential for defining martingales.

### 3.9. Infinitely divisible distributions

probability Durrett

A certain kind of well behaving distributions has characteristic functions that can be represented in canonical form. In this section we cover conditions that such distributions have and its canonical representation.

### 3.10. Limit theorems in ℝᵈ

probability Durrett

This part covers limit theorems regarding random vectors $\mathbf{X} = (X_1,\cdots,X_d)’\in\mathbb{R}^d.$
I would like to finish reviewing Probability theory I by briefly mentioning the Poisson convergence (section 3.6) and limit theorems in $\mathbb{R}^d$ (3.10).