Žitković, Forward-convex convergence in probability of sequences of nonnegative random variables

Abstract. For a sequence (fn)n∈N of nonnegative random variables, we pro-vide simple necessary and sufficient conditions for convergence in probability of each sequence (hn)n∈N with hn ∈ conv({fn, fn+1,...}) for all n ∈ N to the same limit. These conditions correspond to an essentially measure-free version of the notion of uniform integrability