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arXiv · 2111.14678

Attainable forms of intermediate dimensions

Amlan Banaji·Alex Rutar
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Abstract

The intermediate dimensions are a family of dimensions which interpolate between the Hausdorff and box dimensions of sets. We prove a necessary and sufficient condition for a given function $h(\theta)$ to be realized as the intermediate dimensions of a bounded subset of $\mathbb{R}^d$. This condition is a straightforward constraint on the Dini derivatives of $h(\theta)$, which we prove is sharp using a homogeneous Moran set construction.

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Amlan Banaji, Alex Rutar. 2021-11-29. Attainable forms of intermediate dimensions. https://doi.org/10.54330/afm.120529

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