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On the strong convergence of a weighted sum. (English) Zbl 0951.60027
Summary: We prove the equivalence of the almost sure and complete convergence of a particular weighted sum of independent, identically distributed random variables investigated by Y. S. Chow and T. L. Lai [Ann. Probab. 1, 810–824 (1973; Zbl 0303.60025)].

MSC:
60F15 Strong limit theorems
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[1] Chow, Y.S.; Lai, T.L., Limiting behavior of weighted sums of independent random variables, Ann. probab., 1, 810-824, (1973) · Zbl 0303.60025
[2] Chow, Y.S., Teicher, H., 1978. Probability Theory. Springer, New York.
[3] Hsu, P.L.; Robbins, H., Complete convergence and the law of large numbers, Proc. nat. acad. sci. U.S.A., 33, 25-31, (1947) · Zbl 0030.20101
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