1. Let Xl, X2,…, Xn… be independent random variables and let Sn = Formula Presented. In the so-called law of the iterated logarithm, completely solved by Feller recently, the upper limit of Sn as n → ∞ is considered and its true order of magnitude is found with probability one. A counterpart to that problem is to consider the lower limit of Sn as n → ∞ and to make a statement about its order of magnitude with probability one.
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