TY - JOUR
AU - Banaji, Amlan
AU - Rutar, Alex
PY - 2022/07/04
Y2 - 2024/02/25
TI - Attainable forms of intermediate dimensions
JF - Annales Fennici Mathematici
JA - Ann. Fenn. Math.
VL - 47
IS - 2
SE - Articles
DO - 10.54330/afm.120529
UR - https://afm.journal.fi/article/view/120529
SP - 939-960
AB - <pre>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.</pre><p> </p>
ER -