ABSTRACT
The law of large numbers expresses the notion that the mean of a sample from a distribution converges to the mean of the distribution in some sense. When the convergence is in probability or, equivalently, in law, this is known as the weak law of large numbers. When the convergence is almost surely, it is the strong law of large numbers. The simplest law of large numbers, and the most useful for statistical work, is for distributions with finite second moments, and the convergence is in quadratic mean.
