Minkowski dimension for measures
Classical Analysis and ODEs
2024-03-20 v4 Metric Geometry
Abstract
The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literature on the dimension theory of measures. As the terminology suggests, we show that it can be used to characterise the Minkowski dimension of a compact metric space. We also study its relationship with other concepts in dimension theory.
Keywords
Cite
@article{arxiv.2001.07055,
title = {Minkowski dimension for measures},
author = {Kenneth J. Falconer and Jonathan M. Fraser and Antti Käenmäki},
journal= {arXiv preprint arXiv:2001.07055},
year = {2024}
}
Comments
16 pages, 1 figure