A measure theoretic result for approximation by Delone sets
Dynamical Systems
2019-08-19 v2 Metric Geometry
Number Theory
Abstract
With a view to establishing measure theoretic approximation properties of Delone sets, we study a setup which arises naturally in the problem of averaging almost periodic functions along exponential sequences. In this setting, we establish a full converse of the Borel-Cantelli lemma. This provides an analogue of more classical problems in the metric theory of Diophantine approximation, but with the distance to the nearest integer function replaced by distance to an arbitrary Delone set.
Cite
@article{arxiv.1702.04839,
title = {A measure theoretic result for approximation by Delone sets},
author = {Michael Baake and Alan Haynes},
journal= {arXiv preprint arXiv:1702.04839},
year = {2019}
}
Comments
6 pagess, new version with minor revisions and updates