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Completeness with respect to the probabilistic Pompeiu-Hausdorff metric

Stefan Cobzaş
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Abstract

The aim of the present paper is to prove that the family of all closed nonempty subsets of a complete probabilistic metric space $L$ is complete with respect to the probabilistic Pompeiu-Hausdorff metric $H$. The same is true for the families of all closed bounded, respectively compact, nonempty subsets of $L$. If $L$ is a complete random normed space in the sense of Šerstnev, then the family of all nonempty closed convex subsets of $L$ is also complete with respect to $H$.

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Stefan Cobzaş. 2005-07-11. Completeness with respect to the probabilistic Pompeiu-Hausdorff metric. https://arxiv.org/abs/math/0507207

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