Geodesic
On a property of a sequence of events
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 3, pp. 531-534 
M. I. Taksar. On a property of a sequence of events. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 3, pp. 531-534. http://geodesic.mathdoc.fr/item/TVP_1968_13_3_a16/
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     author = {M. I. Taksar},
     title = {On a~property of a~sequence of events},
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     pages = {531--534},
     year = {1968},
     volume = {13},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_3_a16/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\{A_n\}$ be a sequence of events and $\varlimsup\mathbf P(A_n)=p>0$. Then it is possible to choose for any $c<1$ a subsequence with the property: for any $k$, the probability of the intersection of arbitrary $k$ events of the subsequence is more than $cp^k$. This statement becomes false if we replace the constant $c$ by a sequence $c_k\to1$.