Law of Large Numbers

A collection of probabilistic results stating that the sample average of many independent, identically distributed random variables converges (in probability, almost surely, or in some modes) to the common expected value as the sample size grows.

A collection of results stating that sample averages (or empirical means) converge to the population expectation as sample size grows: in probability (weak law) or almost surely (strong law), under conditions such as independence and integrability.

The statistical principle that, under specified conditions (typically sequences of independent or weakly dependent random variables with a finite expected value), the sample average converges to the theoretical expected value as the sample size grows; formalized in weak and strong forms with precise probabilistic limits.