Intermediate dimensions

@article{Falconer2018IntermediateD,
title={Intermediate dimensions},
author={Kenneth J. Falconer and Jonathan M. Fraser and Tom Kempton},
journal={Mathematische Zeitschrift},
year={2018},
volume={296},
pages={813-830}
}
• Published 15 November 2018
• Mathematics
• Mathematische Zeitschrift
We introduce a continuum of dimensions which are ‘intermediate’ between the familiar Hausdorff and box dimensions. This is done by restricting the families of allowable covers in the definition of Hausdorff dimension by insisting that $$|U| \le |V|^\theta$$ | U | ≤ | V | θ for all sets U ,  V used in a particular cover, where $$\theta \in [0,1]$$ θ ∈ [ 0 , 1 ] is a parameter. Thus, when $$\theta =1$$ θ = 1 only covers using sets of the same size are allowable, and we recover the box dimensions…
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