Geodesic
Dimension of a measure
Studia Mathematica, Tome 142 (2000) no. 3, pp. 219-233

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-142-3-219-233

Pertti Mattila 1 ; Manuel Morán 1 ; José-Manuel Rey 1

1 
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Pertti Mattila; Manuel Morán; José-Manuel Rey. Dimension of a measure. Studia Mathematica, Tome 142 (2000) no. 3, pp. 219-233. doi: 10.4064/sm-142-3-219-233

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