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arXiv · 2004.05133

Intermediate Assouad-like dimensions for measures

Kathryn E. Hare·Kevin G. Hare
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Abstract

The upper and lower Assouad dimensions of a metric space are local variants of the box dimensions of the space and provide quantitative information about the `thickest' and `thinnest' parts of the set. Less extreme versions of these dimensions for sets have been introduced, including the upper and lower quasi-Assouad dimensions, $\theta $-Assouad spectrum, and $\Phi $-dimensions. In this paper, we study the analogue of the upper and lower $\Phi $-dimensions for measures. We give general properties of such dimensions, as well as more specific results for self-similar measures satisfying various separation properties and discrete measures.

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Kathryn E. Hare, Kevin G. Hare. 2020-04-10. Intermediate Assouad-like dimensions for measures. https://doi.org/10.1142/s0218348x20501431

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