Exact packing measure of central Cantor sets in the line
type: Item
instance of: scholarly article
title: Exact packing measure of central Cantor sets in the line
zbMATH Open document ID: 1229.28015
author: Ignacio Garcia
author: Leandro Zuberman
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-11-02T00:00:00Z
review text: Hausdorff and packing dimensions are among the two most commonly studied notions of dimension in fractal geometry. Exact computations of the corresponding Hausdorff or packing measure in the critical exponent is typically a challenging problem. For central Cantor sets in the real line, exact Hausdorff measures have been computed by \textit{Ch. Qu, H. Rao} and \textit{W. Su} [Advances in Mathematics Research 2, 75--79 (2003; Zbl 1076.28006)]. In this paper, the authors compute the exact packing measures of a class of symmetric central Cantor sets. As a consequence, they are able to provide information about measure density and centered Hausdorff measures of such sets.
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 5966304
zbMATH Keywords: Cantor set
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: packing measure
zbMATH Keywords: density
reviewed by: Jeremy T. Tyson
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.08.044
OpenAlex ID: W2334631532
cites work: Exact Hausdorff measure and intervals of maximum density for Cantor sets
cites work: On the Complementary Intervals of a Linear Closed Set of Zero Lebesgue Measure
cites work: Classifying Cantor sets by their fractal dimensions
cites work: Q3995301
cites work: Exact packing measure of linear Cantor sets
cites work: The pointwise densities of the Cantor measure
cites work: Dimension functions of Cantor sets
cites work: THE POINTWISE DENSITIES OF NON-SYMMETRIC CANTOR SETS
cites work: Mesures de Hausdorff et théorie de Perron-Frobenius des matrices non- négatives
cites work: Q4328334
cites work: The Hausdorff measure and the packing measure on a perturbed Cantor set
cites work: Density theorems for Hausdorff and packing measures of self-similar sets
cites work: Q4672452
cites work: The upper densities of symmetric perfect sets
cites work: Packing regularity of sets in n-space
cites work: On the pointwise densities of the Cantor measure
DOI: 10.1016/J.JMAA.2011.08.044
description: scientific article; zbMATH DE number 5966304