Attainable forms of intermediate dimensions
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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(θ) to be realized as the intermediate dimensions of a bounded subset of Rd. This condition is a straightforward constraint on the Dini derivatives of h(θ), which we prove is sharp using a homogeneous Moran set construction.
Banaji , A & Rutar , A 2022 , ' Attainable forms of intermediate dimensions ' , Annales Academiae Scientiarum Fennicae-Mathematica , vol. 47 , no. 2 , pp. 939-960 . https://doi.org/10.54330/afm.120529
Annales Academiae Scientiarum Fennicae-Mathematica
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