A measure theoretic result for approximation by Delone sets

Michael Baake, Alan Haynes

Research output: Working paperPreprint


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.
Original languageEnglish
Number of pages6
Publication statusPublished - 16 Feb 2017

Bibliographical note

6 pages


  • math.DS
  • math.MG
  • math.NT
  • 11K06, 52C23

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