Completeness with respect to the probabilistic Pompeiu-Hausdorff metric

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dc.creatorCobzaş, Stefan
dc.date2005-07-11
dc.date.accessioned2026-07-07T05:21:35Z
dc.date.available2026-07-07T05:21:35Z
dc.descriptionThe 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 $H$.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0507207
dc.identifierhttp://arxiv.org/abs/math/0507207
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75741
dc.subjectProbability
dc.subjectGeneral Topology
dc.subject46S50, 54E70
dc.titleCompleteness with respect to the probabilistic Pompeiu-Hausdorff metric
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