Cantor type sets of positive measure and Lipschitz mappings (Q1194672)
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scientific article; zbMATH DE number 68386
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cantor type sets of positive measure and Lipschitz mappings |
scientific article; zbMATH DE number 68386 |
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Cantor type sets of positive measure and Lipschitz mappings (English)
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5 October 1992
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The author proves that there exist nonempty nowhere dense, perfect sets \(E_1,E_2\subset [0,1]\) such that each of their portions is of positive Lebesgue measure and there exists no Lipschitz function \(f: [0,1]\to\mathbb{R}\) satisfying \(f(E_1)=E_2\).
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Cantor type sets
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nowhere dense sets
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perfect sets
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Lipschitz function
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