For countable abelian group actions, Banach-, Weyl- and Besicovitch-mean equicontinuity are equivalent, and transitive almost Banach-mean equicontinuous systems have zero topological entropy.
Auslander, Mean-L-stable systems
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The systems with almost Banach mean equicontinuity for abelian group actions
For countable abelian group actions, Banach-, Weyl- and Besicovitch-mean equicontinuity are equivalent, and transitive almost Banach-mean equicontinuous systems have zero topological entropy.