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Measure-theoretic sequence entropy pairs and mean sensitivity

Published online by Cambridge University Press:  19 September 2023

Universidad Autonoma de San Luis Potosi, San Luis Potosi 78000, Mexico (e-mail: Faculty of Mathematics and Computer Science, Jagiellonian University, Profesora Stanisława Łojasiewicza 6, 30-348 Kraków, Poland
Universidad Autonoma de San Luis Potosi, San Luis Potosi 78000, Mexico (e-mail:


We characterize measure-theoretic sequence entropy pairs of continuous actions of abelian groups using mean sensitivity. This addresses an open question of Li and Yu [On mean sensitive tuples. J. Differential Equations 297 (2021), 175–200]. 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.

Original Article
© The Author(s), 2023. Published by Cambridge University Press

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