Equivalences are proven for diam-mean and mean equicontinuity between a system and its measure-induced version, while hyperspace versions require separate conditions with explicit counterexamples.
Ergodic Theory Dynam
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Mean Equicontinuity and Related Properties in Hyperspace and Measure Dynamics
Equivalences are proven for diam-mean and mean equicontinuity between a system and its measure-induced version, while hyperspace versions require separate conditions with explicit counterexamples.