Archiv der Mathematik

, Volume 106, Issue 3, pp 237–246 | Cite as

A note on the distribution of the digits in Cantor expansions



Let \({\{x_n\}_n}\) be the digits of the Cantor expansion of \({x \in [0,1]}\) with respect to a sequence of integers \({\{q_n\}_n}\) with \({q_n \ge 2}\). In this paper, we prove that the set consisting of those points for which the set of limit points of \({\{x_n/q_n\}_n}\) equals to [0, 1] is residual in [0, 1] if \({\lim\nolimits_{n \to \infty}q_n = +\infty}\).


Cantor expansion Residual set Inhomogeneous symbolic space 

Mathematics Subject Classification

11K55 37B10 28A80 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsMinnan Normal UniversityZhangzhouPeople’s Republic of China
  2. 2.School of Statistics and MathematicsZhongnan University of Economics and LawWuhanPeople’s Republic of China
  3. 3.Department of MathematicsSouth China University of TechnologyGuangzhouPeople’s Republic of China

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