How do the typical \(L^q\)-dimensions of measures behave? (Q2926585)
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scientific article; zbMATH DE number 6363207
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | How do the typical \(L^q\)-dimensions of measures behave? |
scientific article; zbMATH DE number 6363207 |
Statements
31 October 2014
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dimensions
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measures
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multifractal analysis
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Hausdorff measure
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How do the typical \(L^q\)-dimensions of measures behave? (English)
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For a compact set \(K\subset \mathbb{R}^{d}\) the author computes the value of the upper and of the lower \(L_{q}\)-dimension of a typical probability measure with a support contained in \(K\) for any \(q\in \mathbb{R}\). Different definitions of the ``dimension'' of \(K\) are involved in computing these values, following \(q\in \mathbb{R}\). The paper is very technical and the techniques of the proofs are hard.
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