Lois du logarithme itéré avec pondérations additives

Tenenbaum, Gérald

doi:10.1090/S0002-9939-09-10035-7

Lois du logarithme itéré avec pondérations additives
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by Gérald Tenenbaum PDF

Proc. Amer. Math. Soc. 137 (2009), 4255-4257 Request permission

Abstract:

We provide a very short proof that natural Lindeberg type conditions on the non-negative arithmetic additive function $f$ ensure the strong law of large numbers and the law of the iterated logarithm for weighted sums $\sum _{n\leqslant N}f(n)X_n$ for any sequence $\{X_n\}_{n=1}^\infty$ of i.i.d. random variables.

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