Mathematics > Dynamical Systems
[Submitted on 23 Mar 2022 (v1), last revised 31 Aug 2024 (this version, v5)]
Title:Measure-theoretic metric mean dimension
View PDF HTML (experimental)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.
Submission history
From: Rui Yang [view email][v1] Wed, 23 Mar 2022 07:50:41 UTC (12 KB)
[v2] Sun, 8 May 2022 03:23:16 UTC (15 KB)
[v3] Thu, 10 Nov 2022 08:53:27 UTC (14 KB)
[v4] Mon, 15 May 2023 03:35:06 UTC (13 KB)
[v5] Sat, 31 Aug 2024 08:24:27 UTC (19 KB)
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