The pointwise dimensions of Moran measures
type: Item
instance of: scholarly article
title: The pointwise dimensions of Moran measures
zbMATH Open document ID: 1200.28011
author: J. Martínez
published in: Science China. Mathematics
publication date: 2010-08-23T00:00:00Z
review text: The calculation of the Hausdorff dimension of a fractal set is in many cases very difficult to execute. Much of the theory of Hausdorff and packing dimension of sets depends on local properties of a suitably defined measure. The lower pointwise dimension of the measure is related to the Hausdorff dimension and the upper pointwise dimension is related to the packing dimension. So it is important to consider the pointwise dimension of a measure in the study of fractals. In this paper the authors extend the known pointwise dimension results of some self-similar measures and Moran measures. The main results are contained in Theorems 2.7, 2.8 and 2.9, where formulas of upper (lower) pointwise dimensions of some Moran measures on Moran sets in \(\mathbb R^d\) are obtained under the strong separation condition. Also, formulas for the dimension of the Moran measures are derived. Some examples are given at the end of the paper. The paper is very well written and the subject is interesting and up to date.
reviewed by: Nicolae-Adrian Secelean
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 37C45
zbMATH DE Number: 5774123
zbMATH Keywords: pointwise dimension
zbMATH Keywords: Moran measure
zbMATH Keywords: Moran set
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: packing dimension
zbMATH Keywords: self-similar sets
MaRDI profile type: Publication
full work available at URL: s11425-010-0127-2
OpenAlex ID: W2053191199
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DOI: 10.1007/S11425-010-0127-2
description: scientific article; zbMATH DE number 5774123