Hausdorff measure of the scattered Cantor sets
type: Item
instance of: scholarly article
zbMATH Open document ID: 1007.28006
author: Hung Hwan Lee
author: In-Soo Baek
publication date: 2002-04-08T00:00:00Z
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1725452
zbMATH Keywords: scattered Cantor sets
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: Hausdorff dimension
MaRDI profile type: Publication
title: Hausdorff measure of the scattered Cantor sets
published in: Kyungpook Mathematical Journal
review text: The authors consider an invariant of the classical Cantor set: the relative position of basic intervals may change arbitrarily at each generation, but keep the same scaling 1/3 and open set condition. It is easy to see that the Hausdorff dimension of this class of sets is \(\frac{\log 2}{\log 3}\). Then the authors estimate the Hausdorff measure in dimension \(\frac{\log 2}{\log 3}\) of this class, which in general differs from 1 (the Hausdorff measure of the classical Cantor set).
reviewed by: Hua Su
description: scientific article; zbMATH DE number 1725452