PROBABILISTIC ARZELA-ASCOLI THEOREM

Mohammed Bachir (1) , Nazaret Bruno

1 Dynamique et contrôl Optimal

We prove that, in the space of all probabilistic continuous functions from a probabilistic metric space G to the set ∆ + of all cumulative distribution functions vanishing at 0, the space of all 1-Lipschitz functions is compact if and only if the space G is compact. This gives a probabilistic Arzela-Ascoli type Theorem.

Keywords: Probabilistic metric space; Probabilistic 1-Lipschitz map; Probabilistic Arzela-Ascoli type Theorem; msc: 54E70; 46S50

Domains: Mathematics [math]; Functional Analysis [math.FA]

Mohammed Bachir, Nazaret Bruno. PROBABILISTIC ARZELA-ASCOLI THEOREM. 2019. ⟨hal-02112322v1⟩