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Teoriya Veroyatnostei i ee Primeneniya, 1968, Volume 13, Issue 3, Pages 531–534 (Mi tvp879)  
Short Communications

On a property of a sequence of events

M. I. Taksar

Moscow
Full-text PDF (272 kB)
Abstract: 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 $c_k\to1$.
Received: 17.12.1966
English version:
Theory of Probability and its Applications, 1968, Volume 13, Issue 3, Pages 501–504
DOI: https://doi.org/10.1137/1113064
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. I. Taksar, “On a property of a sequence of events”, Teor. Veroyatnost. i Primenen., 13:3 (1968), 531–534; Theory Probab. Appl., 13:3 (1968), 501–504
Citation in format AMSBIB
\Bibitem{Tak68}
\by M.~I.~Taksar
\paper On a~property of a~sequence of events
\jour Teor. Veroyatnost. i Primenen.
\yr 1968
\vol 13
\issue 3
\pages 531--534
\mathnet{http://mi.mathnet.ru/tvp879}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=238363}
\zmath{https://zbmath.org/?q=an:0167.17301}
\transl
\jour Theory Probab. Appl.
\yr 1968
\vol 13
\issue 3
\pages 501--504
\crossref{https://doi.org/10.1137/1113064}
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