Completeness with respect to the probabilistic Pompeiu-Hausdorff metric

Details Completeness with respect to the probabilistic Pompeiu-Hausdorff metric Completeness with respect to the probabilistic Pompeiu-Hausdorff metric

2005-07-11

arxiv.org/abs/math/0507207v1

Mathematics

Probability

17 pages

Scientific paper

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 \v{S}erstnev, then the family of all nonempty closed convex subsets of $L$ is also complete with respect to $H$.

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