Amenable Metric Mean Dimension and Amenable Mean Hausdorff Dimension of Product Sets and Metric Varying
Xianqiang Li, Xiaofang Luo
TL;DR
This paper studies how metric mean dimension and mean Hausdorff dimension vary with metrics for amenable group actions, extending previous results and establishing product formulas for these dimensions.
Contribution
It extends the understanding of metric mean and Hausdorff dimensions' continuity and proves product formulas for amenable group actions.
Findings
Continuity of metric mean and Hausdorff dimensions with respect to metrics.
Product formulas for mean Hausdorff and metric mean dimensions.
Extension of previous results to amenable group actions.
Abstract
Metric mean dimension and mean Hausdorff dimension depend on metrics. In this paper, we investigate the continuity of the metric mean dimension and mean Hausdorff dimension concerning the metrics for amenable group actions, which extends recent results by Muentes, Becker, Baraviera et al.. Moreover, we give proof of the product formulas for the mean Hausdorff dimension and the metric mean dimension for amenable group actions.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical Dynamics and Fractals · Optimization and Variational Analysis