Complex Systems

Besicovitch Pseudodistances with Respect to
Non-Følner Sequences Download PDF

Silvio Capobianco
Department of Software Science
Tallinn University of Technology,

Pierre Guillon
CNRS, Aix-Marseille Université
Institut de Mathématiques de Marseille


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 Følner sequence, then every shift is an isometry. For non-Følner sequences, it is proved that some shifts are not isometries, and the Besicovitch pseudodistance with respect to some subsequences even makes them discontinuous.

Keywords: Besicovitch distance; Følner sequences; submeasures; amenability; non-compact space; symbolic dynamics  

Cite this publication as:
S. Capobianco and P. Guillon, “Besicovitch Pseudodistances with Respect to Non-Følner Sequences,” Complex Systems, 30(2), 2021 pp. 133–158.