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.
Original languageEnglish
Pages (from-to)939-960
JournalAnnales Academiae Scientiarum Fennicae-Mathematica
Issue number2
Publication statusPublished - 4 Jul 2022


  • Hausdorff dimension
  • Box dimension
  • Intermediate dimensions
  • Moran set


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