The sequence of variates with corresponding means obeys the strong law of large numbers if, to every pair , there corresponds an such that there is probability or better that for every , all inequalities
(1)
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for , , ..., will be satisfied, where
(2)
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(3)
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(Feller 1968). Kolmogorov established that the convergence of the sequence
(4)
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sometimes called the Kolmogorov criterion, is a sufficient condition for the strong law of large numbers to apply to the sequence of mutually independent random variables with variances (Feller 1968).