Geodesic
The law of iterated logarithm for Cesaro's and Abel's methods of summation
Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 449-459

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Let $\{x_k\}$ be a set of independent random variables bounded in common with means 0 and variations 1. The analogues of the law of iterated logarithm for the $(C,\alpha)$ $(\alpha>0)$ and $A$ methods of summation are proved (see theorems 2 and 3). 
@article{TVP_1965_10_3_a3,
     author = {V. F. Gaposhkin},
     title = {The law of iterated logarithm for {Cesaro's} and {Abel's} methods of summation},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {449--459},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1965},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a3/}
}
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V. F. Gaposhkin. The law of iterated logarithm for Cesaro's and Abel's methods of summation. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 449-459. http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a3/