Continuous maps that preserve Hausdorff measure

被引：0

作者：

Deng, Da-Wen ^{[1
]}

Huang, Yulan ^{[2
]}

Ngai, Sze-Man ^{[3
,4
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China

[2] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

[3] Hunan Normal Univ, Coll Math & Stat, Key Lab High Performance Comp & Stochast Informat, Minist Educ China, Changsha 410081, Hunan, Peoples R China

[4] Georgia Southern Univ, Dept Math Sci, Statesboro, GA 30460 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 516卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Hausdorff measure; Homeomorphism; Cantor set; Self-similar set; Cantor dust; LIPSCHITZ EQUIVALENCE;

D O I：

10.1016/j.jmaa.2022.126485

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the space of homeomorphisms on the unit interval [0, 1], equipped with the topology of uniform convergence, contains a dense subspace of functions that preserve the Hausdorff measure of any subset of certain one-dimensional self-similar sets. We extend the results to a class of Cantor dust type self-similar sets in R-2. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：10

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