Geodesic
An improvement of the lower bound for the rate of convergence in the Kolmogorov's uniform limit theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 4, pp. 767-772

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An estimate obtained in [2] is improved. This result together with [1] means that the rate of convergence in the Kolmogorov's uniform limit theorem is of the order $n^{-1/2}$. 
@article{TVP_1982_27_4_a10,
     author = {T. V. Arak},
     title = {An improvement of the lower bound for the rate of convergence in the {Kolmogorov's} uniform limit theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {767--772},
     publisher = {mathdoc},
     volume = {27},
     number = {4},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_4_a10/}
}
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T. V. Arak. An improvement of the lower bound for the rate of convergence in the Kolmogorov's uniform limit theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 4, pp. 767-772. http://geodesic.mathdoc.fr/item/TVP_1982_27_4_a10/