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arXiv · 2001.11306

Intermediate value property for the Assouad dimension of measures

Ville Suomala
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Abstract

Hare, Mendivil, and Zuberman have recently shown that if $X$ is a compact subset of the reals and of non-zero Assouad dimension $\dim_A X$, then for all $s>\dim_A X$, $X$ supports measures with Assouad dimension $s$. We generalise this result to arbitrary complete metric spaces.

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Ville Suomala. 2020-01-30. Intermediate value property for the Assouad dimension of measures. https://arxiv.org/abs/2001.11306

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