Let $X_1,X_2,\dots$ be a sequence of independent random variables, with finite expectations. The strong law of large numbers holds if one of the following conditions is satisfied:

1. The random variables are identically distributed;
2. For each $n$ the variance of $X_n$ is finite, and $$\sum_{n=1}^\infty \frac{\operatorname{Var}[X_n]}{n^2} <\infty.$$