# Moment conditions in strong laws of large numbers for multiple sums and random measures

14 Aug 2017 Klesov Oleg Molchanov Ilya

The validity of the strong law of large numbers for multiple sums $S_n$ of independent identically distributed random variables $Z_k$, $k\leq n$, with $r$-dimensional indices is equivalent to the integrability of $|Z|(\log^+|Z|)^{r-1}$, where $Z$ is the typical summand. We consider the strong law of large numbers for more general normalisations, without assuming that the summands $Z_k$ are identically distributed, and prove a multiple sum generalisation of the Brunk--Prohorov strong law of large numbers... (read more)

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