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.
@article{bwmeta1.element.bwnjournal-article-smv142i3p219bwm,
author = {Pertti Mattila and Manuel Mor\'an and Jos\'e-Manuel Rey},
title = {Dimension of a measure},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {219-233},
zbl = {1008.28005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv142i3p219bwm}
}
Mattila, Pertti; Morán, Manuel; Rey, José-Manuel. Dimension of a measure. Studia Mathematica, Tome 141 (2000) pp. 219-233. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv142i3p219bwm/
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