Strong Law of Large Numbers

For a set of random variates $x_i$ from a distribution having unit Mean,

$$P\left({\,\lim_{n\to \infty}{x_1+\ldots +x_n\over n}}\right)... ...\,\lim_{n\to \infty}\left\langle{x}\right\rangle{}}\right)= 1.$$

This result is due to Kolmogorov.

See also Law of Truly Large Numbers, Strong Law of Small Numbers, Weak Law of Large Numbers