For amenable group actions, IE-tuples of the induced measure system equal the closed convex hull of IE-tuples of the original system, with partial analogues for IN and IT tuples and a sharp n ≤ C log m embedding bound for ℓ_q^n inside ℓ_∞^m.
Independence, sequence entropy and mean sensitivity for invariant measures
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We investigate the connections between independence, sequence entropy, and mean sensitivity for a measure preserving system under the action of a countable infinite discrete group. We establish that every sequence entropy tuple for an invariant measure is an IT tuple. Furthermore, if the acting group is amenable, we show that for an ergodic measure, the sequence entropy tuples, the mean sensitive tuples along some tempered F{\o}lner sequence, and the sensitive in the mean tuples along some tempered F{\o}lner sequence coincide.
citation-role summary
background 1
citation-polarity summary
fields
math.DS 1years
2025 1verdicts
ACCEPT 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Local entropy theory, combinatorics, and local theory of Banach spaces
For amenable group actions, IE-tuples of the induced measure system equal the closed convex hull of IE-tuples of the original system, with partial analogues for IN and IT tuples and a sharp n ≤ C log m embedding bound for ℓ_q^n inside ℓ_∞^m.