On topologies connected with Hausdorff measures (Q930114)
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scientific article; zbMATH DE number 5291261
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On topologies connected with Hausdorff measures |
scientific article; zbMATH DE number 5291261 |
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On topologies connected with Hausdorff measures (English)
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20 June 2008
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The author proves that for every \(s\in(0,1)\) there exists a~set \(E\subseteq\mathbb R\) of Hausdorff dimension~\(s\) such that its \(s\)-dimensional Hausdorff measure is not \(\sigma\)-finite. As a~consequence she obtains strict inclusions for a~variety of \(\sigma\)-ideals connected with Hausdorff measures. She also compares the density topologies associated with Hausdorff measures.
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Hausdorff measures
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density topologies
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\(\sigma\)-ideals
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