On one fractal property of the Minkowski function

  • Symon Serbenyuk
Original Paper


The article is devoted to fractal properties of the singular Minkowski function. It is proved that this function does not belong to the class of DP-transformations, i.e., the Minkowski function does not preserve the Hausdorff–Besicovitch dimension.


Singular function Fractal Self-similar set Hausdorff–Besicovitch dimension Minkowski function 

Mathematics Subject Classification

28A80 26A30 11K55 03E99 11K50 


Compliance with ethical standards

Conflict of interest

The author declares that he has no competing interests.


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Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  1. 1.Institute of MathematicsNational Academy of Sciences of UkraineKyivUkraine

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