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THE SPACE OF PROBABILISTIC 1-LIPSCHITZ MAPS

Mohammed Bachir 1, 2
1 Equations d'evolution
SAMM - 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 : Saturday, December 30, 2017 - 7:20:16 AM
Last modification on : Friday, May 6, 2022 - 4:50:07 PM

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  • HAL Id : hal-01673497, version 1
  • ARXIV : 1801.00581

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Mohammed Bachir. THE SPACE OF PROBABILISTIC 1-LIPSCHITZ MAPS. 2017. ⟨hal-01673497v1⟩

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