Minkowski dimension for measures
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.
Citation
Falconer , K J , Fraser , J & Käenmäki , A 2023 , ' Minkowski dimension for measures ' , Proceedings of the American Mathematical Society , vol. 151 , no. 2 , pp. 779-794 . https://doi.org/10.1090/proc/16174
Publication
Proceedings of the American Mathematical Society
Status
Peer reviewed
ISSN
0002-9939Type
Journal article
Description
Funding: JMF and KJF are financially supported by an EPSRC Standard Grant (EP/R015104/1) and JMF by a Leverhulme Trust Research Project Grant (RPG-2019-034).Collections
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