0.1 Laws of Large Numbers
The weak and strong laws of large numbers a fundamental results in probability theory detailing the convergence in probability and almost surely respectively of the sample mean of random variables defined by \[ \frac{S_{n}}{n}=\frac{{X_{1}+\dots+X_{n}}}{n}. \] The proof for both results rely on Chebychev Inequality and the proof of the strong law requires the Borel-Cantelli Lemma.
There are various versions of the laws of large numbers with various strength conditions.
Weak Laws of Large Numbers Strong Law of Large Numbers