The other form of this theorem applies if the sum of all variances divided by the index squared converges; that is known as the Kolmogorov criterion, and applies to the strong version of this theorem, which adds that the convergence is almost sure.
Markov's inequality can be used with Chebyshev's inequality to derive one form of this law, a form that also leads to the asymptotic equipartition property. The other form of this theorem applies if the sum of all variances divided by the index squared converges; that is known as the Kolmogorov criterion, and applies to the strong version of this theorem, which adds that the convergence is almost sure. With a name coined by Simeon Poisson, identify this law that states that as n approaches infinity, the arithmetic mean of n random variables converges to its expected value.
Markov's inequality can be used with Chebyshev's inequality to derive one form of this law, a form that also leads to the asymptotic equipartition property.
law of {large numbers} [accept “{weak}” or “{strong}” as a {modifier}; accept {Bernoulli's Theorem}]