The Hausdorff dimension of sets related to the general Sierpinski carpets

Yong Xin Gui; Wen Xia Li

doi:10.1007/s10114-010-7453-8

The Hausdorff dimension of sets related to the general Sierpinski carpets

Yong Xin Gui
, Wen Xia Li

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper we study a class of subsets of the general Sierpinski carpets for which the allowed two digits in the expansions occur with proportional frequency. We calculate the Hausdorff and box dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive finite.

Original language	English
Pages (from-to)	731-742
Number of pages	12
Journal	Acta Mathematica Sinica, English Series
Volume	26
Issue number	4
DOIs	https://doi.org/10.1007/s10114-010-7453-8
State	Published - Apr 2010

Keywords

General Sierpinski carpets
Hausdorff dimension
Hausdorff measure

Access to Document

10.1007/s10114-010-7453-8

Cite this

@article{d8ec066dd9764271908aa652cbe86396,

title = "The Hausdorff dimension of sets related to the general Sierpinski carpets",

abstract = "In this paper we study a class of subsets of the general Sierpinski carpets for which the allowed two digits in the expansions occur with proportional frequency. We calculate the Hausdorff and box dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive finite.",

keywords = "General Sierpinski carpets, Hausdorff dimension, Hausdorff measure",

author = "Gui, \{Yong Xin\} and Li, \{Wen Xia\}",

year = "2010",

month = apr,

doi = "10.1007/s10114-010-7453-8",

language = "英语",

volume = "26",

pages = "731--742",

journal = "Acta Mathematica Sinica, English Series",

issn = "1439-8516",

publisher = "Springer Verlag",

number = "4",

}

TY - JOUR

T1 - The Hausdorff dimension of sets related to the general Sierpinski carpets

AU - Gui, Yong Xin

AU - Li, Wen Xia

PY - 2010/4

Y1 - 2010/4

N2 - In this paper we study a class of subsets of the general Sierpinski carpets for which the allowed two digits in the expansions occur with proportional frequency. We calculate the Hausdorff and box dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive finite.

AB - In this paper we study a class of subsets of the general Sierpinski carpets for which the allowed two digits in the expansions occur with proportional frequency. We calculate the Hausdorff and box dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive finite.

KW - General Sierpinski carpets

KW - Hausdorff dimension

KW - Hausdorff measure

UR - https://www.scopus.com/pages/publications/77952813828

U2 - 10.1007/s10114-010-7453-8

DO - 10.1007/s10114-010-7453-8

M3 - 文章

AN - SCOPUS:77952813828

SN - 1439-8516

VL - 26

SP - 731

EP - 742

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 4

ER -

The Hausdorff dimension of sets related to the general Sierpinski carpets

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this