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arXiv · 1904.12514

Probabilistic Arzela-Ascoli theorem

Mohammed Bachir·Nazaret Bruno
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Abstract

We prove that, in the space of all probabilistic continuous functions from a probabilistic metric space G to the set $\Delta$ + 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.

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Mohammed Bachir, Nazaret Bruno. 2019-04-29. Probabilistic Arzela-Ascoli theorem. https://arxiv.org/abs/1904.12514

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