Attainable forms of intermediate dimensions
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(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.
Citation
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
Publication
Annales Academiae Scientiarum Fennicae-Mathematica
Status
Peer reviewed
ISSN
1239-629XType
Journal article
Rights
Copyright (c) 2022 Annales Fennici Mathematici. Open Access. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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