On the absolute continuity of a class of invariant measures (Q2759025)
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scientific article; zbMATH DE number 1680685
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the absolute continuity of a class of invariant measures |
scientific article; zbMATH DE number 1680685 |
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On the absolute continuity of a class of invariant measures (English)
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10 December 2001
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absolute continuity
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invariant measure
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iterated function system
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eigen-measures
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conformal IFS
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Hausdorff measure
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Radon-Nikodým derivative
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The authors compare eigen-measures of a conformal IFS with variable weights to the natural Hausdorff measure. Under the condition that the invariant compact set of the IFS is an \(s\)-set, the absolute continuity of the eigen-measure with respect to the \(s\)-Hausdorff measure implies that both measures are equivalent. The \(p\)-th integrability of the Radon-Nikodým derivative of the eigen-measure is also studied.
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