Geodesic
On the multidimensional central limit theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 1, pp. 164-170

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Two estimations in the central limit theorem for equally distributed random vectors in $R^s$ are given. The first one involves distribution functions (for $s=2$) and is an improvement of previous results stated in [1] and [2]. The second one concerns (for arbitrary $s$) “the distance” $\rho_2$ defined as $$ \sup_A|P(A)-Q(A)| $$ where the supremum is taken over all measurable convex sets $A\in R^s$ (cf. [5]). 
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     author = {S. M. Sadikova},
     title = {On the multidimensional central limit theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {164--170},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a14/}
}
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S. M. Sadikova. On the multidimensional central limit theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 1, pp. 164-170. http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a14/