Geodesic
The~law of large numbers and the~logarithmic law for arrays
Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 195-206.

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In this paper we study the asymptotic behavior of sums for arrays of i.i.d. random variables. We obtain conditions under which the law of large numbers for subsequences holds and give an example showing the impossibility to weaken them. Also we establish an analogue of the law of the iterated logarithm. 
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     author = {A. E. Mikusheva},
     title = {The~law of large numbers and the~logarithmic law for arrays},
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A. E. Mikusheva. The~law of large numbers and the~logarithmic law for arrays. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 195-206. http://geodesic.mathdoc.fr/item/FPM_2000_6_1_a15/