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.
|Number of pages||4|
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|State||Published - 8 Apr 2001|
- Cantor sets
- Diophantine approximation
- Very-well-approximable numbers