Concerning a real-valued continuous function on the interval with graph of Hausdorff dimension 2 (Q1902491)
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scientific article; zbMATH DE number 819167
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Concerning a real-valued continuous function on the interval with graph of Hausdorff dimension 2 |
scientific article; zbMATH DE number 819167 |
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Concerning a real-valued continuous function on the interval with graph of Hausdorff dimension 2 (English)
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1 February 1996
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Summary: A real-valued continuous nowhere-differentiable function on \([0,1]\) is constructed. Its graph \(F\) is proved to have the following property. If \(B\) is a Borel subset of \(F\) and if the projection of \(B\) on \([0,1]\) has positive Lebesgue measure, then the Hausdorff dimension of \(B\) is two.
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graph
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real-valued continuous nowhere-differentiable function
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Hausdorff dimension
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