Research output: Working paper

**A measure theoretic result for approximation by Delone sets.** / Baake, Michael; Haynes, Alan.

Research output: Working paper

Baake, M & Haynes, A 2017 'A measure theoretic result for approximation by Delone sets'. <https://arxiv.org/abs/1702.04839>

Baake, M., & Haynes, A. (2017). *A measure theoretic result for approximation by Delone sets*. https://arxiv.org/abs/1702.04839

Baake M, Haynes A. A measure theoretic result for approximation by Delone sets. 2017 Feb 16.

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title = "A measure theoretic result for approximation by Delone sets",

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.",

keywords = "math.DS, math.MG, math.NT, 11K06, 52C23",

author = "Michael Baake and Alan Haynes",

note = "6 pages",

year = "2017",

month = feb,

day = "16",

language = "English",

type = "WorkingPaper",

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AU - Baake, Michael

AU - Haynes, Alan

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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.

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KW - math.MG

KW - math.NT

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M3 - Working paper

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