Abstract
In this paper we formulate the notions of upper metric mean dimension and upper measure-theoretic mean dimension for amenable group actions. In particular, a different version of variational principle for amenable group actions is presented by replacing the condition on the space in Velozo and Velozo (Rate distortion theory, metric mean dimension and measure theoretic entropy. Preprint ArXiV: 1707.05762 [Math.DS], 2017) by the conditions on the systems. At last, we discuss the relation between upper metric mean dimensions and pseudo-orbits.
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