Probabilistic Arzela-Ascoli theorem
Functional Analysis
2019-04-30 v1
Abstract
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.
Cite
@article{arxiv.1904.12514,
title = {Probabilistic Arzela-Ascoli theorem},
author = {Mohammed Bachir and Nazaret Bruno},
journal= {arXiv preprint arXiv:1904.12514},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1801.00581