Almost no points on a Cantor set are very well approximable (Q2748039)
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scientific article; zbMATH DE number 1658842
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Almost no points on a Cantor set are very well approximable |
scientific article; zbMATH DE number 1658842 |
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Almost no points on a Cantor set are very well approximable (English)
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20 October 2002
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Cantor set
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Diophantine approximation
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In this note a form of Khinchin's theorem on \(\psi\)-approximable numbers is shown for certain measures supported on fractal subsets of the reals. A striking application of the result is to show that with respect to the measure supported on the middle-thirds Cantor set obtained by choosing ternary digits 0,1,2 with probability \(1/2\), \(0\), \(1/2\) respectively, almost every real is not very well approximable.
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