Geodesic
Some comments on multidimensional local limit theorems
Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 559-563 Cet article a éte moissonné depuis la source Math-Net.Ru

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A proof is given of a theorem on monotonic approximation of continuous functions in $H_k$, $1\le k$, with compact carriers. The obtained theorem is employed to prove multidimensional local limit theorems. 
@article{MZM_1973_14_4_a13,
     author = {A. V. Nagaev},
     title = {Some comments on multidimensional local limit theorems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {559--563},
     year = {1973},
     volume = {14},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a13/}
}
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A. V. Nagaev. Some comments on multidimensional local limit theorems. Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 559-563. http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a13/