Some remarks on the Hausdorff measure of the Cantor set

In this paper, the author further reveals some intrinsic properties of the Cantor set. By the properties, the author gives a new method for calculating the exact value of the Hausdorff measure of the Cantor set, and shows the facts that each covering which consists of basic intervals, in which any b...

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Main Author:	Wang Minghua
Format:	Article
Language:	English
Published:	EDP Sciences 2016-01-01
Series:	SHS Web of Conferences
Subjects:	fractal Hausdorff measure Cantor set
Online Access:	http://dx.doi.org/10.1051/shsconf/20162401015

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spelling	doaj-ab380ef2c92846bc9ee8b6cf4de45e5d2021-02-02T07:06:33ZengEDP SciencesSHS Web of Conferences2261-24242016-01-01240101510.1051/shsconf/20162401015shsconf_sshe2016_01015Some remarks on the Hausdorff measure of the Cantor setWang MinghuaIn this paper, the author further reveals some intrinsic properties of the Cantor set. By the properties, the author gives a new method for calculating the exact value of the Hausdorff measure of the Cantor set, and shows the facts that each covering which consists of basic intervals, in which any basic interval cannot completely contain the other, is the best covering of the Cantor set, and the Hausdorff measure of the Cantor set can be determined by coverings which only consist of basic intervals.http://dx.doi.org/10.1051/shsconf/20162401015fractalHausdorff measureCantor set
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Wang Minghua
spellingShingle	Wang Minghua Some remarks on the Hausdorff measure of the Cantor set SHS Web of Conferences fractal Hausdorff measure Cantor set
author_facet	Wang Minghua
author_sort	Wang Minghua
title	Some remarks on the Hausdorff measure of the Cantor set
title_short	Some remarks on the Hausdorff measure of the Cantor set
title_full	Some remarks on the Hausdorff measure of the Cantor set
title_fullStr	Some remarks on the Hausdorff measure of the Cantor set
title_full_unstemmed	Some remarks on the Hausdorff measure of the Cantor set
title_sort	some remarks on the hausdorff measure of the cantor set
publisher	EDP Sciences
series	SHS Web of Conferences
issn	2261-2424
publishDate	2016-01-01
description	In this paper, the author further reveals some intrinsic properties of the Cantor set. By the properties, the author gives a new method for calculating the exact value of the Hausdorff measure of the Cantor set, and shows the facts that each covering which consists of basic intervals, in which any basic interval cannot completely contain the other, is the best covering of the Cantor set, and the Hausdorff measure of the Cantor set can be determined by coverings which only consist of basic intervals.
topic	fractal Hausdorff measure Cantor set
url	http://dx.doi.org/10.1051/shsconf/20162401015
work_keys_str_mv	AT wangminghua someremarksonthehausdorffmeasureofthecantorset
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Some remarks on the Hausdorff measure of the Cantor set

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