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On one fractal property of the Minkowski function

  • Symon Serbenyuk
Original Paper
  • 64 Downloads

Abstract

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.

Keywords

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

Mathematics Subject Classification

28A80 26A30 11K55 03E99 11K50 

Notes

Compliance with ethical standards

Conflict of interest

The author declares that he has no competing interests.

References

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    Serbenyuk S. O.: Preserving the Hausdorff–Besicovitch dimension by monotonic singular distribution functions. In: Second interuniversity scientific conference on mathematics and physics for young scientists: abstracts, pp. 106–107. Institute of Mathematics of NAS of Ukraine, Kyiv (2011). https://www.researchgate.net/publication/301637057 (in Ukrainian)

Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

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

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