Summary
For double arrays of constants {ani,1≦i≦k n ,n≧1} and i.i.d. random variables X,X i ,i≧1, conditions are given under which the row sums \(\sum\limits_{i = 1}^{k_n } {a_{ni} } X_i \xrightarrow{{{\text{a}}{\text{.c}}{\text{.}}}}0\). Both cases k n ↑∞ and k n =∞ are treated. In general, the hypotheses involve a trade-off between moment requirements on X and the magnitude of the {itani}. A Marcinkiewicz-Zygmund type strong law is obtained for the special case
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Research supported by National Science Foundation under Grant MCS-8005481.
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Teicher, H. Almost certain convergence in double arrays. Z. Wahrscheinlichkeitstheorie verw Gebiete 69, 331–345 (1985). https://doi.org/10.1007/BF00532738
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DOI: https://doi.org/10.1007/BF00532738