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.
Keywords:
Hausdorff dimension, box dimension, intermediate dimensions, Moran set
Affiliations des auteurs :
Amlan Banaji
1
;
Alex Rutar
1
1
University of St Andrews, Mathematical Institute
Amlan Banaji; Alex Rutar. Attainable forms of intermediate dimensions. Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 939-960. doi: 10.54330/afm.120529
@article{AFM_2022_47_2_a15,
author = {Amlan Banaji and Alex Rutar},
title = {Attainable forms of intermediate dimensions},
journal = {Annales Fennici Mathematici},
pages = {939--960},
year = {2022},
volume = {47},
number = {2},
doi = {10.54330/afm.120529},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.54330/afm.120529/}
}
TY - JOUR
AU - Amlan Banaji
AU - Alex Rutar
TI - Attainable forms of intermediate dimensions
JO - Annales Fennici Mathematici
PY - 2022
SP - 939
EP - 960
VL - 47
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.54330/afm.120529/
DO - 10.54330/afm.120529
LA - en
ID - AFM_2022_47_2_a15
ER -
%0 Journal Article
%A Amlan Banaji
%A Alex Rutar
%T Attainable forms of intermediate dimensions
%J Annales Fennici Mathematici
%D 2022
%P 939-960
%V 47
%N 2
%U http://geodesic.mathdoc.fr/articles/10.54330/afm.120529/
%R 10.54330/afm.120529
%G en
%F AFM_2022_47_2_a15
