Hausdorff dimensions of sets related to Lüroth expansion

Y. Gui; W. Li

doi:10.1007/s10474-016-0661-7

Hausdorff dimensions of sets related to Lüroth expansion

Y. Gui, W. Li

School of Mathematical Sciences

Hubei University of Science and Technology

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

4 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	286-302
Number of pages	17
Journal	Acta Mathematica Hungarica
Volume	150
Issue number	2
DOIs	https://doi.org/10.1007/s10474-016-0661-7
State	Published - 1 Dec 2016

Keywords

primary 28A80
secondary 28A78

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abstract = "We study two classes of sets of real numbers related to L{\"u}roth expansions and obtain their Hausdorff dimensions. One is determined by prescribed group frequencies of digits in their L{\"u}roth 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 L{\"u}roth expansion. The other is determined by randomly selecting the digits in their L{\"u}roth expansion from a finite number of given digit sets.",

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AB - 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.

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ER -

Hausdorff dimensions of sets related to Lüroth expansion

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