# ON THE PRUSS EXTENSION OF THE HSU-ROBBINS-ERD S THEOREM

• Sung, Soo-Hak (Department of Applied Mathematics, Pai Chai University)
• Published : 1999.05.01

#### Abstract

The Hsu-Robbins-erd s theorem states that if {$X_m,n\geq1$} is a sequence of independent and identically distributed random variables, then ${EX_1}^2<\infty$ and $EX_1$=0 if and only if ${\sum_{n=1}}^\infty\;P($\mid${\sum_{k=1}}^nX_k$\mid$\geqn\in)<\infty$ for every $\in$ > 0. Under some auxiliary conditions, Sp taru (1994) extended this to the case where the $X_n$ are independent, but their distributions come from a finite set. Pruss (1996) proved Sp taru's result under weaker conditions, The purpose of this paper is to improve Pruss conditions.

#### References

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