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arXiv · 2203.12251

Measure-theoretic metric mean dimension

Rui Yang·Ercai Chen·Xiaoyao Zhou
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Abstract

For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $\epsilon$-entropies, and show that measure-theoretic metric mean dimensions of different types of measure-theoretic $\epsilon$-entropies coincide with the packing metric mean dimension of the set of generic points of ergodic measures.

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Rui Yang, Ercai Chen, Xiaoyao Zhou. 2022-03-23. Measure-theoretic metric mean dimension. https://arxiv.org/abs/2203.12251

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