Kolmogorov Strong Law of Large Numbers
# Statement
Let $(\Omega, \mathcal{B}, \mathbb{P})$ be a Probability Space and let $(X_{n}){n=1}^{\infty}$ be a Sequence of iid Random Variables on $\Omega$. Let $S{n} = \sum\limits_{i=1}^{n} X_{n}$. Then there exists $c \in \mathbb{R}$ s.t. $\frac{S_{n}}{n} \to c$ a.s. If and Only If $\mathbb{E}|X_{1}| < \infty$, in which case $c = \mathbb{E}(X_{1})$.
# Proof
TODO - See thm 7.5.1 in Resnick - A Probability Path pg 220