Geodesic
On a weak form of a local limit theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 3, pp. 648-653 
A. B. Muhin. On a weak form of a local limit theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 3, pp. 648-653. http://geodesic.mathdoc.fr/item/TVP_1976_21_3_a18/
@article{TVP_1976_21_3_a18,
     author = {A. B. Muhin},
     title = {On a~weak form of a~local limit theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {648--653},
     year = {1976},
     volume = {21},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_3_a18/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\{\xi_{nk}\}$ be a sequence of series of independent random variables. In the paper, a limit theorem for $$ \mathbf P\biggl\{\sum_{k=1}^n\xi_{nk}\in\biggl[x-\frac{\lambda_n}{2},x+\frac{\lambda_n}{2}\biggr]\biggr\}, $$ where $\displaystyle\lambda_n=o\biggl(\sum_{k=1}^n\mathbf D\xi_{nk}\biggr)$, is obtained