Download PDF - Dimension of a measure
ArticleOriginal scientific text
Title
Dimension of a measure
Authors 1, 2, 2
Affiliations
- Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland
- Departamento de Análisis Económico, Universidad Complutense, Campus de Somosaguas, 28223 Madrid, Spain
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.
Bibliography
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Pages:
219-233
Main language of publication
English
Received
1999-02-04
Accepted
1999-04-29
Published
2000
Exact and natural sciences