THE SPACE OF PROBABILISTIC 1-LIPSCHITZ MAPS

Mohammed Bachir (1, 2)

1 Equations d'evolution
2 UP1 - Université Paris 1 Panthéon-Sorbonne

We introduce and study a natural notion of probabilistic 1-Lipschitz maps. We prove that the space of all probabilistic 1-Lipschitz maps defined on a probabilistic metric space G is also a probabilistic metric space. Moreover, when G is a group, then the space of all prob-abilistic 1-Lipschitz maps defined on G can be endowed with a monoid structure. Then, we caracterize the probabilistic invariant complete Menger groups by the space of all probabilistic 1-Lipschitz maps in the sprit of the classical Banach-Stone theorem.

Mots clés: Probabilistic metric space; Probabilistic 1-Lipschitz map; Proba- bilistic Banach-Stone type theorem and Isometries msc: 46S50; 47S50; 54E70

Domaines: Analyse fonctionnelle [math.FA]

Mohammed Bachir. THE SPACE OF PROBABILISTIC 1-LIPSCHITZ MAPS. 2018. ⟨hal-01673497v2⟩