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Zero-infinity laws in Diophantine approximation

Bugeaud, Y., Dodson, M.M. and Kristensen, S. (2005) Zero-infinity laws in Diophantine approximation. The Quarterly Journal of Mathematics, 56 (3). pp. 311-320. ISSN 1464-3847

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It is shown that for any translation invariant outer measure M, the M-measure of the intersection of any subset of Rn that is invariant under rational translations and which does not have full Lebesgue measure with the closure of an open set of positive measure cannot be positive and finite. Analogues for p-adic fields and fields of formal power series over a finite field are established. The results are applied to some problems in metric Diophantine approximation.

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 11 Feb 2009 10:16
Last Modified: 11 Feb 2009 10:16
Published Version: http://dx.doi.org/10.1093/qmath/hah043
Status: Published
Publisher: Oxford University Press
Identification Number: 10.1093/qmath/hah043
URI: http://eprints.whiterose.ac.uk/id/eprint/7777

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