A sequence of random variables $X_1, X_2,\dots$ with finite expectations in a probability space is said to satisfiy the strong law of large numbers if

$$ \frac{1}{n}\sum_{k=1}^n (X_k -\operatorname{E}[X_k]) \xrightarrow[]{a.s.} 0, $$

where $a.s.$ stands for convergence almost surely.

When the random variables are identically distributed, with expectation $\mu$ , the law becomes:

$$ \frac{1}{n}\sum_{k=1}^n X_k\xrightarrow[]{a.s.} \mu.$$

Kolmogorov's strong law of large numbers theorems give conditions on the random variables under which the law is satisfied.