Discrete spectrum, bounded measure complexity, and the two mean-equicontinuity notions coincide for invariant measures of countable amenable group actions, with the equicontinuity parts requiring tempered Følner sequences.
Halmos and John von Neumann, Operator methods in classical mechanics
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Discrete spectrum for amenable group actions
Discrete spectrum, bounded measure complexity, and the two mean-equicontinuity notions coincide for invariant measures of countable amenable group actions, with the equicontinuity parts requiring tempered Følner sequences.