The pointwise dimension of self-similar measures in complete metric spaces
type: Item
instance of: scholarly article
title: The pointwise dimension of self-similar measures in complete metric spaces
zbMATH Open document ID: 1095.28010
author: Chen Ercai
author: Tassilo Küpper
published in: Chaos, Solitons and Fractals
publication date: 2005-04-21T00:00:00Z
review text: For a probability measure \(\mu\) on a complete metric space \(X\), the pointwise dimension of \(\mu\) at \(x \in X\) is given by \[ d_\mu(x):=\lim_{r \to 0} \frac{\log \mu(B(x,r))}{\log r} \] provided that the limit exists. In the paper, the pointwise dimension of self-similar measures is investigated under the condition that the strong open set condition is satisfied.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 2160084
zbMATH Keywords: pointwise dimension of a measure
zbMATH Keywords: Hausdorff dimension of a measure
zbMATH Keywords: self-similar measure
zbMATH Keywords: (strong) open set condition
reviewed by: Uta Freiberg
MaRDI profile type: Publication
full work available at URL: j.chaos.2004.02.020
OpenAlex ID: W2075692648
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DOI: 10.1016/J.CHAOS.2004.02.020
description: scientific article; zbMATH DE number 2160084