Geodesic
Unconditional convergence of Gaussian random series in Banach spaces
Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 1, pp. 178-182

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A sufficient condition is given for the a.s. unconditional convergence of Gaussian series in Banach spaces with unconditional bases not containing $l^n_\infty$'s uniformly. By the a.s. unconditional convergence of random series we understand the convergence of all rearrangements of the series on the same set of total probability.
Keywords: a.s. unconditional convergence, Gaussian series, Banach spaces, not containing $l^n_\infty$'s uniformly. 
@article{TVP_2000_45_1_a10,
     author = {V. V. Kvaratskheliya},
     title = {Unconditional convergence of {Gaussian} random series in {Banach} spaces},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {178--182},
     publisher = {mathdoc},
     volume = {45},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_1_a10/}
}
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V. V. Kvaratskheliya. Unconditional convergence of Gaussian random series in Banach spaces. Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 1, pp. 178-182. http://geodesic.mathdoc.fr/item/TVP_2000_45_1_a10/