Geodesic
On connection between the local and integral theorems for latticed distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 1, pp. 175-179

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In the present paper a sequence of independent integer random variables is constructed which satisfies the integral limit theorem, is asymptotically uniformly distributed and has the infinite smallness property, but the local theorem fails to be valid for it. Thus Yu. V. Prohorov's hypothesis that the conditions enumerated be sufficient for the local theorem is refuted. 
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     author = {N. G. Gamkrelidze},
     title = {On connection between the local and integral theorems for latticed distributions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {175--179},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a16/}
}
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N. G. Gamkrelidze. On connection between the local and integral theorems for latticed distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 1, pp. 175-179. http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a16/