# The space of probabilistic $1$-Lipschitz maps

1 Equations d'evolution
SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
Abstract : We introduce and study the natural notion of probabilistic $1$-Lipschitz maps. We use the space of all probabilistic $1$-Lipschitz maps to give a new method for the construction of probabilistic metric completion (respectively of probabilistic invariant metric group completion). Our construction is of independent interest. We prove that the space of all probabilistic $1$-Lipschitz maps defined on a probabilistic invariant metric group can be endowed with a monoid structure. Next, we explecite the set of all invertible element of this monoid and characterize the probabilistic invariant complete Menger groups by the space of all probabilistic $1$-Lipschitz maps in the sprit of the classical Banach-Stone theorem.
Document type :
Journal articles
Domain :

https://hal-paris1.archives-ouvertes.fr/hal-01973212
Contributor : Mohammed Bachir <>
Submitted on : Tuesday, January 8, 2019 - 11:06:50 AM
Last modification on : Wednesday, January 20, 2021 - 3:21:37 PM

### Identifiers

• HAL Id : hal-01973212, version 1

### Citation

Mohammed Bachir. The space of probabilistic $1$-Lipschitz maps. Aequationes Mathematicae, Springer Verlag, 2019, 93 (5), pp.955-983. ⟨hal-01973212⟩

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