Measure-theoretic sequence entropy pairs and mean sensitivity

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.

arXiv comment12 pages

References in corpus (5)

• Bounded complexity, mean equicontinuity and discrete spectrum
• Mean sensitive, mean equicontinuous and almost periodic functions for dynamical systems
• Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group
• Sequence entropy tuples and mean sensitive tuples
• Local entropy theory and descriptive complexity

Cited by in corpus (1)

• Sequence entropy tuples and mean sensitive tuples