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MR2109818 60F15 (60F05)
Giuliano Antonini, Rita; Pratelli, Luca A strong law of large numbers for generalized almost sure central limit theorems. Teor. Ĭmovīr. Mat. Stat. No. 70 (2004), 1--8; translation in Theory Probab. Math. Statist. No. 70 (2005), 1–9
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