A characterization of {\mu}-equicontinuity for topological dynamical systems
Dynamical Systems
2019-11-05 v6
Abstract
Two different notions of {\mu}-equicontinuity that apply to topological dynamical systems and probability measures were studied by Gilman (1987) and Huang-Lu-Ye (2011). One was used to classify measure preserving topological dynamical systems and the other for cellular automata. We show that if the probability space satisfies Lebesgue's density theorem and Vitali's covering theorem (for example a Cantor set or a subset of R^{d}) then both properties are equivalent. To do this we characterize when a function is Lusin measurable.
Keywords
Cite
@article{arxiv.1309.0467,
title = {A characterization of {\mu}-equicontinuity for topological dynamical systems},
author = {Felipe García-Ramos},
journal= {arXiv preprint arXiv:1309.0467},
year = {2019}
}
Comments
Original preprint was divided in two papers