Measure-theoretic sequence entropy pairs and mean sensitivity

Felipe García-Ramos, Victor Muñoz-López

Published 2022-10-26Version 1

We characterize measure-theoretic sequence entropy pairs of continuous abelian group actions using mean sensitivity. This solves an open question mentioned by Li and Yu. As a consequence of our results we provide a simpler characterization of Kerr and Li's independence sequence entropy pairs ($\mu$-IN-pairs) when the measure is ergodic and the group is abelian.