A measure theoretic result for approximation by Delone sets

TY - UNPB

T1 - A measure theoretic result for approximation by Delone sets

AU - Baake, Michael

AU - Haynes, Alan

N1 - 6 pages

PY - 2017/2/16

Y1 - 2017/2/16

N2 - 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.

AB - 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.

KW - math.DS

KW - math.MG

KW - math.NT

KW - 11K06, 52C23

M3 - Preprint

BT - A measure theoretic result for approximation by Delone sets

ER -