## Almost certain convergence in double arrays.(English)Zbl 0548.60028

For double arrays of constants $$\{a_{ni}$$, $$1\leq i\leq k_ n,n\geq 1\}$$ and i.i.d. random variables $$\{X,X_ i$$, $$i\geq 1\}$$, conditions are given under which the row sums $$\sum^{k_ n}_{i=1}a_{ni}X_ i\to^{a.c.}0$$. Both cases $$k_ n\uparrow\infty$$ and $$k_ n=\infty$$ are treated. In general, the hypotheses involve a trade-off between moment requirements on X and the magnitude of the $$\{a_{ni}\}$$. A Marcinkiewicz-Zygmund type strong law is obtained for the special case $$a_{ni}=a_ i/(\sum^{n}_{j=1}a^ p_ j)^{1/p}$$, $$a_ i>0$$, $$\sum^{n}_{1}a^ p_ j\to\infty$$, $$0<p<2$$.

### MSC:

 60F15 Strong limit theorems
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### References:

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