## A note on the strong law of large numbers for associated sequences.(English)Zbl 1087.60510

Summary: We prove that the sequence $$\{b_n^{-1}\sum^n_{i=1}(X_i-EX_i)\}_{n\geq 1}$$ converges a.e.  to zero if $$\{X_n,n\geq 1\}$$ is an associated sequence of random variables with $$\sum^\infty_{n=1} b_{k_n}^{-2}\text{Var}(\sum^{k_n}_{i=k_n+1}X_i) <\infty$$ where $$\{b_n,n\geq 1\}$$ is a positive nondecreasing sequence and $$\{k_n, n\geq 1\}$$ is a strictly increasing sequence, both tending to infinity as $$n$$ tends to infinity and $$0<a=\inf_{n\geq 1}b_{k_n}b_{k_{n+1}}^{-1}\leq \sup_{n\geq 1} b_{k_n}b_{k_{n+1}}^{-1}=c<1$$.

### MSC:

 60F15 Strong limit theorems
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