THE SPACE OF PROBABILISTIC 1-LIPSCHITZ MAPS

Mohammed Bachir 1, 2
1 Equations d'evolution
SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
Abstract : 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.
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Submitted on : Tuesday, January 16, 2018 - 9:38:09 PM
Last modification on : Thursday, January 18, 2018 - 1:18:44 AM

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  • HAL Id : hal-01673497, version 2
  • ARXIV : 1801.00581

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

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