Abstract
We obtain the Erdős–Rényi type law of large numbers for "nonconventional" sums of the form $S_n=\sum_{m=1}^nF(X_m,X_{2m},...,X_{\ell m})$ where $X_1,X_2,...$ is a sequence of i.i.d. random variables and $F$ is a bounded Borel function. The proof relies on nonconventional large deviations obtained in a previous work.
Citation
Yuri Kifer. "An Erdős–Rényi law for nonconventional sums." Electron. Commun. Probab. 20 1 - 8, 2015. https://doi.org/10.1214/ECP.v20-4613
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