Measure-theoretic metric mean dimension

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 $\hat{I}\mu$-entropies, and show that measure-theoretic metric mean dimensions of different types of measure-theoretic $\hat{I}\mu$-entropies coincide with the packing metric mean dimension of the set of generic points of ergodic measures.

Final version