Geodesic
On the convergence of martingales and geometric properties of Banach spaces
Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 2, pp. 385-391 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we give a condition which implies the almost sure convergence of a class of martingales with values in a uniformly 2-smooth Banach space. This condition is also necessary if martingales take values in a uniformly 2-convex Banach space. These results allow us to characterize the Hilbert space in terms of the almost sure convergence of martingales. 
@article{TVP_1981_26_2_a12,
     author = {Dang Hung Thang and Nguen Duy Tien},
     title = {On the convergence of martingales and geometric properties of {Banach} spaces},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {385--391},
     year = {1981},
     volume = {26},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a12/}
}
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Dang Hung Thang; Nguen Duy Tien. On the convergence of martingales and geometric properties of Banach spaces. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 2, pp. 385-391. http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a12/