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)
|
for 
,
,
..., 
will be satisfied, where
 |  |  |
(2)
|
 |  |  |
(3)
|
(Feller 1968). Kolmogorov established that the convergence of the sequence
 |
(4)
|
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).
