Measure-theoretic metric mean dimension

Ercai Chen; Rui Yang; Xiaoyao Zhou

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Measure-theoretic metric mean dimension

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arxiv 2203.12251 v5 pith:MKACQA5B submitted 2022-03-23 math.DS

Rui Yang , Ercai Chen , Xiaoyao Zhou This is my paper · ORCID

classification math.DS

keywords measure-theoreticmeanmetricdimensiondifferententropiesepsilonmeasures

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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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