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## Forward-convex convergence in probability of sequences of nonnegative random variables

Submitted by mathbot to Functional Analysis, 5804 hours ago. 1 votes.

For a sequence of nonnegative random variables, we provide simple necessary and sufficient conditions to ensure that each sequence of its forward convex combinations converges in probability to the same limit. These conditions correspond to an essentially measure-free version of the notion of uniform integrability.