Dimension of a measure (Q2717536)
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scientific article; zbMATH DE number 1605126
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dimension of a measure |
scientific article; zbMATH DE number 1605126 |
Statements
Dimension of a measure (English)
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17 June 2001
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Borel measures
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monotonicity
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bi-Lipschitz invariance
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\((\sigma-)\)stability
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measure dimensions
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correlation dimensions
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We propose a framework to define dimensions of Borel measures in a metric space by formulating a set of natural properties for a measure-dimension mapping, namely monotonicity, bi-Lipschitz invariance, (\(\sigma\)-)stability, etc. We study the behaviour of most popular definitions of measure dimensions in regard to our list, with special attention to the standard correlation dimensions and their modified versions.
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