Hausdorff dimensions of sets related to Lüroth expansion

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• 作者：Y. Gui ; W. Li
• 关键词：Mathematics Subject Classificationprimary 28A80 ; secondary 28A78
• 刊名：Acta Mathematica Hungarica
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：150
• 期：2
• 页码：286-302
• 全文大小：832 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Sciences
  Mathematics
  
• 出版者：Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
• ISSN：1588-2632
• 卷排序：150

文摘

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.