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  • 1 Mathematical Institute of the Hungarian Academy of Sciences P.O. Box 127 H-1364 Budapest Hungary
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LetSn be the partial sums of ?-mixing stationary random variables and letf(x) be a real function. In this note we give sufficient conditions under which the logarithmic average off(Sn/sn) converges almost surely to ?-88f(x)dF(x). We also obtain strong approximation forH(n)=?k=1nk-1f(Sk/sk)=logn ?-88f(x)dF(x) which will imply the asymptotic normality ofH(n)/log1/2n. But for partial sums of i.i.d. random variables our results will be proved under weaker moment condition than assumed for ?-mixing random variables.

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