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Multifractal analysis for the pointwise Assouad dimension of self-similar measures

We quantify the pointwise doubling properties of self-similar measures using the notion of pointwise Assouad dimension. We show that all self-similar measures satisfying the open set condition are pointwise doubling in a set of full Hausdorff dimension, despite the fact that they can in general be non-doubling in a set of full Hausdorff measure. More generally, we carry out multifractal analysis by determining the Hausdorff dimension of the level sets of the pointwise Assouad dimension.

preprint2024arXivOpen access
Roope AnttilaVille Suomala
math.DSmath.CA
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Roope AnttilaVille Suomala

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