Perfekte Mengen mit unterschiedlicher Hausdorff- und unterer metrischer Dimension (Q760519)
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scientific article; zbMATH DE number 3884418
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Perfekte Mengen mit unterschiedlicher Hausdorff- und unterer metrischer Dimension |
scientific article; zbMATH DE number 3884418 |
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Perfekte Mengen mit unterschiedlicher Hausdorff- und unterer metrischer Dimension (English)
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1985
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It is proved that in every complete metric space (M,d) there exist perfect sets whose Hausdorff dimension is strictly less than the lower metric dimension. In particular, the same inequality is established in \({\mathbb{R}}\) for the corresponding local dimensions, thus solving a problem of Vosburg. An appropriate example is exhibited.
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perfect sets whose Hausdorff dimension is strictly less than the lower metric dimension
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local dimensions
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0.8869114
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0.8812486
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0.8613887
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0.8455059
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