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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

© 1996-9 Eric W. Weisstein