Hausdorff dimensions of sets related to Luroth expansion

被引：4

作者：

Gui, Y. ^{[1
]}

Li, W. ^{[2
]}

机构：

[1] HuBei Univ Sci & Technol, Sch Math & Stat, Xianning 437100, Peoples R China

[2] East China Normal Univ, Shanghai Key Lab PMMP, Dept Math, Shanghai 200241, Peoples R China

来源：

ACTA MATHEMATICA HUNGARICA | 2016年 / 150卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Luroth expansion; group frequency; Hausdorff dimension;

D O I：

10.1007/s10474-016-0661-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study two classes of sets of real numbers related to Luroth expansions and obtain their Hausdorff dimensions. One is determined by prescribed group frequencies of digits in their Luroth expansions. It is proved that the Hausdorff dimension of such a set is equal to the supremum of the Hausdorff dimensions for sets of real numbers with prescribed digit frequencies in their Luroth expansion. The other is determined by randomly selecting the digits in their Luroth expansion from a finite number of given digit sets.

引用

页码：286 / 302

页数：17

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