The Vitali Covering Theorem in the Weihrauch Lattice

Vasco Brattka, Guido Gherardi, Rupert Hölzl, Arno Pauly

Published 2016-05-11Version 1

We study the uniform computational content of the Vitali Covering Theorem for intervals using the tool of Weihrauch reducibility. We show that a more detailed picture emerges than what a related study by Giusto, Brown, and Simpson has revealed in the setting of reverse mathematics. In particular, different formulations of the Vitali Covering Theorem turn out to have different uniform computational content. These versions are either computable or closely related to uniform variants of Weak Weak K\H{o}nig's Lemma.