Geodesic
Relationship between local and integral limit theorems
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 96-110

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The double array of independent finite-dimensional random vectors is considered. Conditions are studied under which the weak convergence of distributions of centered and normalized sums to an absolutely continuous distribution implies the validity of the local limit theorem for the probability of falling of the non-normalized sum into a bounded domain and the latter theorem implies the local limit theorem for densities.
Keywords: sums of independent random variables, operator normalization, integral limit theorem, local limit theorems. 
@article{TVP_1995_40_1_a4,
     author = {A. B. Mukhin},
     title = {Relationship between local and integral limit theorems},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {96--110},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a4/}
}
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A. B. Mukhin. Relationship between local and integral limit theorems. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 96-110. http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a4/