Almost no points on a Cantor set are very well approximable

Barak Weiss

doi:10.1098/rspa.2000.0700

Almost no points on a Cantor set are very well approximable

Barak Weiss

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

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 language	English
Pages (from-to)	949-952
Number of pages	4
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	457
Issue number	2008
DOIs	https://doi.org/10.1098/rspa.2000.0700
State	Published - 8 Apr 2001

Keywords

Cantor sets
Diophantine approximation
Fractals
Very-well-approximable numbers

ASJC Scopus subject areas

General Mathematics
General Engineering
General Physics and Astronomy

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10.1098/rspa.2000.0700

Cite this

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AB - 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.

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KW - Diophantine approximation

KW - Fractals

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Almost no points on a Cantor set are very well approximable

Abstract

Keywords

ASJC Scopus subject areas

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