Hausdorff dimensions of sets related to Lüroth expansion

被引：0
|
作者：
Y. Gui
W. Li
机构：
[1] HuBei University of Science and Technology,School of Mathematics and Statistics
[2] East China Normal University,Department of Mathematics, Shanghai Key Laboratory of PMMP
来源：
Acta Mathematica Hungarica | 2016年 / 150卷
关键词：
primary 28A80; secondary 28A78; Lüroth expansion; group frequency; Hausdorff dimension;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study two classes of sets of real numbers related to Lüroth expansions and obtain their Hausdorff dimensions. One is determined by prescribed group frequencies of digits in their Lüroth 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 Lüroth expansion. The other is determined by randomly selecting the digits in their Lüroth expansion from a finite number of given digit sets.
引用
收藏
页码：286 / 302
页数：16
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