Geodesic
Note on Gaussian measures in a Banach space
Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 3, pp. 519-520 
A. V. Skorokhod. Note on Gaussian measures in a Banach space. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 3, pp. 519-520. http://geodesic.mathdoc.fr/item/TVP_1970_15_3_a6/
@article{TVP_1970_15_3_a6,
     author = {A. V. Skorokhod},
     title = {Note on {Gaussian} measures in {a~Banach} space},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {519--520},
     year = {1970},
     volume = {15},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_3_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mu$ be a Gaussian measure in a separable Banach space $X$. It is proved that for some $\alpha>0$ $$ \int e^{\alpha\|x\|}\mu(dx)<\infty. $$