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.
Publisher
Finnish Mathematical Society
Cited by
3 articles.
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1. Generalised intermediate dimensions;Monatshefte für Mathematik;2023-07-18
2. Dimensions of popcorn-like pyramid sets;Journal of Fractal Geometry;2023-04-09
3. Intermediate dimensions of infinitely generated attractors;Transactions of the American Mathematical Society;2023-01-24