Abstract
We quantify the pointwise doubling properties of self-similar measures using the notion of pointwise Assouad di-mension. 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.
| Original language | English |
|---|---|
| Pages (from-to) | 1721-1748 |
| Number of pages | 28 |
| Journal | Indiana University Mathematics Journal |
| Volume | 74 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 19 Dec 2025 |
Keywords
- Doubling measure
- Multifractal analysis
- Pointwise Assouad dimension
- Self-similar measure
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