Attainable forms of intermediate dimensions
Avainsanat:
Hausdorff dimension, box dimension, intermediate dimensions, Moran setAbstrakti
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.
Viittaaminen
Banaji, A., & Rutar, A. (2022). Attainable forms of intermediate dimensions. Annales Fennici Mathematici, 47(2), 939–960. https://doi.org/10.54330/afm.120529
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