Besicovitch Pseudodistances with Respect to Non-Følner Sequences
- 15 June 2021
- journal article
- research article
- Published by Wolfram Research, Inc. in Complex Systems
- Vol. 30 (2), 133-158
- https://doi.org/10.25088/complexsystems.30.2.133
Abstract
The Besicovitch pseudodistance defined in [1] for biinfinite sequences is invariant by translations. We generalize the definition to arbitrary locally compact second-countable groups and study how properties of the pseudodistance, including invariance by translations, are determined by those of the sequence of sets of finite positive measure used to define it. In particular, we restate from [2] that if the Besicovitch pseudodistance comes from an exhaustive Folner sequence, then every shift is an isometry. For non-Folner sequences, it is proved that some shifts are not isometries, and the Besicovitch pseudodistance with respect to some subsequences even makes them discontinuous.Keywords
This publication has 1 reference indexed in Scilit:
- Generalized Besicovitch and Weyl spaces: Topology, patterns, and sliding block codesTheoretical Computer Science, 2011