Geodesic
On the Local Limit Theorem for Lattice Distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 4, pp. 733-736 Cet article a éte moissonné depuis la source Math-Net.Ru

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Yu. V. Prokhorov made a conjecture that the two statements are equivalent: (a) the local limit theorem is applicable to a sequence of integer-valued random variables, (b) these variables obey the central limit theorem and their sums are asymptotically uniformly distributed modulo $h$ for arbitrary $h$.We give an example showing that the above conjecture does not hold true. 
@article{TVP_1964_9_4_a15,
     author = {N. G. Gamkrelidze},
     title = {On the {Local} {Limit} {Theorem} for {Lattice} {Distributions}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {733--736},
     year = {1964},
     volume = {9},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_4_a15/}
}
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N. G. Gamkrelidze. On the Local Limit Theorem for Lattice Distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 4, pp. 733-736. http://geodesic.mathdoc.fr/item/TVP_1964_9_4_a15/