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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 {\it Y. S. Chow} and {\it T. L. Lai} [Ann. Probab. 1, 810--824 (1973; Zbl 0303.60025)].

60F15Strong limit theorems
Full Text: DOI
[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. USA 33, 25-31 (1947) · Zbl 0030.20101