2005/07/11 by Ştefan Cobzaş, Stefan Cobzaş, Cobzaş, Stefan
Mathematics · #46S50 #54E70 #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Equations Stability Results #General Topology (math.GN) #Probability (math.PR) #math.GN #math.PR #msc:46S50 #msc:54E70
paper · pdf · doi:10.48550/arxiv.math/0507207
17 pages
arxiv created 2005/07/11 · openalex publication_date 2005/07/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.