Minkowski dimension for measures

Author:

Falconer Kenneth,Fraser Jonathan,Käenmäki Antti

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.

Funder

Engineering and Physical Sciences Research Council

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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