Measure-theoretic metric mean dimension
Volume 280 / 2025
Studia Mathematica 280 (2025), 1-25
MSC: Primary 37A15; Secondary 37C45
DOI: 10.4064/sm230622-9-9
Published online: 27 December 2024
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.
