Every set of positive measure has a porous subset with difference set containing an interval (Q1124001)
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scientific article; zbMATH DE number 4110991
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Every set of positive measure has a porous subset with difference set containing an interval |
scientific article; zbMATH DE number 4110991 |
Statements
Every set of positive measure has a porous subset with difference set containing an interval (English)
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1989
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It is proven that for every set \(A\subset R\) of positive Lebesgue measure and \(p\in (0,1/3)\) there exists a p-porous set \(B\subset A\) such that \(B- B:=\{b-b';b,b'\in B\}\) contains an interval. This theorem is analogous to a Miller's category theorem.
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measurable set
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set of second category
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Baire property
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p-porous set
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Miller's category theorem
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0.8499603867530823
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0.7282642722129822
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