From the same journal

Zero-infinity laws in Diophantine approximation

Research output: Contribution to journalArticlepeer-review


  • Y. Bugeaud
  • M.M. Dodson
  • S. Kristensen


Publication details

JournalThe Quarterly Journal of Mathematics
DatePublished - 23 May 2005
Issue number3
Number of pages9
Pages (from-to)311-320
Original languageEnglish


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.

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