HAL CCSD
Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem
Bachir, Mohammed
Bruno, Nazaret
Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM) ; Université Paris 1 Panthéon-Sorbonne (UP1)
International audience
ISSN: 0166-8641
Topology and its Applications
Elsevier
hal-03075552
https://paris1.hal.science/hal-03075552
https://paris1.hal.science/hal-03075552
Topology and its Applications, 2021, 289
en
[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
info:eu-repo/semantics/article
Journal articles
This work is devoted to the metrization of probabilistic spaces. More precisely, given such a space $(G,D,\star)$ and provided that the triangle function $\star$ is continuous, we exhibit an explicit and canonical metric $\sigma_D$ on $G$ such that the associated topology is homeomorphic to the so-called strong topology. As applications, we make advantage of this explicit metric to present some fixed point theorems on such probabilistic metric structures and we prove a probabilistic version of the Arzela-Ascoli theorem.
2021