Geodesic
Growth of sums of pairwise independent random variables with infinite means
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 2, pp. 382-385 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that $\textbf P\{|S_n|>a_n$ infinitely often$\}=0$ or $1$ if the series $\sum_{n=1}^{\infty}\textbf P\{|X_n|>a_n\}$ is convergent or nonconvergent, where $S_n=X_1+\dots+X_n$ is a sum of identically distributed pairwise independent random variables with infinite expectations, $a_n>0$, for some $m$ a sequence $\{a_n\}_{n\ge m}$ strictly increasing and convex.
Keywords: random variable, pairwise independence. 
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V. M. Kruglov. Growth of sums of pairwise independent random variables with infinite means. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 2, pp. 382-385. http://geodesic.mathdoc.fr/item/TVP_2006_51_2_a7/

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