Measure-theoretic sequence entropy pairs and mean sensitivity

TL;DR

This paper links measure-theoretic sequence entropy pairs with mean sensitivity in continuous abelian group actions, providing simpler characterizations and solving an open question in the field.

Contribution

It introduces a novel characterization of measure-theoretic sequence entropy pairs via mean sensitivity and simplifies the understanding of independence sequence entropy pairs for ergodic measures.

Findings

Characterizes measure-theoretic sequence entropy pairs using mean sensitivity.

Provides a simpler characterization of Kerr and Li's $ ext{μ}$-IN-pairs for ergodic measures.

Solves an open question posed by Li and Yu.

Abstract

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.