Geodesic
On the closeness of moments in normal approximation in Hilbert space
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 2, pp. 251-263

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The rate of convergence of absolute moments in the central limit theorem in Hilbert space is estimated. Theorem 1 improves and extends some of our recent results obtained in [1]. 
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     author = {B. A. Zalesskiǐ and V. V. Sazonov},
     title = {On the closeness of moments in normal approximation in {Hilbert} space},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {251--263},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_2_a3/}
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B. A. Zalesskiǐ; V. V. Sazonov. On the closeness of moments in normal approximation in Hilbert space. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 2, pp. 251-263. http://geodesic.mathdoc.fr/item/TVP_1983_28_2_a3/