# Criteria for the strong law of large numbers for sequences of arbitrary random vectors

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## Abstract

In the following note we obtain sufficient conditions so that the strong law of large numbers would hold for an arbitrary sequence of random variables taking values in a separable Banach space. The conditions are sharp in the sense that they imply the strong law for 2-exchangeable random vectors and they become necessary when the random vectors are pairwise independent, identically distributed.

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