Dimension of a measure
Volume 142 / 2000
Studia Mathematica 142 (2000), 219-233
DOI: 10.4064/sm-142-3-219-233
Abstract
We propose a framework to define dimensions of Borel measures in a metric space by formulating a set of natural properties for a measure-dimension mapping, namely monotonicity, bi-Lipschitz invariance, (σ-)stability, etc. We study the behaviour of most popular definitions of measure dimensions in regard to our list, with special attention to the standard correlation dimensions and their modified versions.
