Almost no points on a Cantor set are very well approximable

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Abstract

We prove that almost no numbers in Cantor's middle-thirds set are very well approximable by rationals. More generally, we discuss Diophantine properties of almost every point, where 'almost every' is understood relative to any measure on the real line satisfying a decay condition introduced in the work of Veech.

Original languageEnglish
Pages (from-to)949-952
Number of pages4
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume457
Issue number2008
DOIs
StatePublished - 8 Apr 2001
Externally publishedYes

Keywords

  • Cantor sets
  • Diophantine approximation
  • Fractals
  • Very-well-approximable numbers

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