Geodesic
Marcinkiewicz–Zygmund laws for Banach space valued random variables with multidimensional parameters
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 213-219 Cet article a éte moissonné depuis la source Math-Net.Ru

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For finite-dimensional array $X(m)=X(m_1,\dots,m_k)$ of independent identically distributed Banach space valued random variables we consider sums $S(n)=S(n_1,\dots,n_k)$ of $X(m)$ over $m_i\in\{1,\dots,n_i\}$ $(i-1,\dots,k)$. Under some conditions on individual random variable $X$ and on the geometry of Banach space the strong law of large numbers for $S(n)$ and estimates for large deviations as $\max n_i\to\infty$ are obtained.
Keywords: Banach space valued random Variables, law of large numbers for multidimensional sums, large deviation probabilities. 
@article{TVP_1995_40_1_a18,
     author = {Nguyen Van Giang},
     title = {Marcinkiewicz{\textendash}Zygmund laws for {Banach} space valued random variables with multidimensional parameters},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {213--219},
     year = {1995},
     volume = {40},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a18/}
}
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Nguyen Van Giang. Marcinkiewicz–Zygmund laws for Banach space valued random variables with multidimensional parameters. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 213-219. http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a18/