Attainable forms of intermediate dimensions

Kirjoittajat

  • Amlan Banaji University of St Andrews, Mathematical Institute
  • Alex Rutar University of St Andrews, Mathematical Institute

Avainsanat:

Hausdorff dimension, box dimension, intermediate dimensions, Moran set

Abstrakti

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.

 

Osasto
Articles

Julkaistu

2022-07-04

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