Zero-infinity laws in Diophantine approximation

Title	Zero-infinity laws in Diophantine approximation
Publication Type	Journal Article
Year of Publication	2005
Authors	Bugeaud Y, Dodson MM, Kristensen S
Journal	Quart. J Math.
Volume	56
Pagination	311-320
Abstract	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.
DOI	10.1093/qmath/hah043

Department of Mathematics