On one fractal property of the Minkowski function
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.
- Publication:
-
Revista Real Acad. Ciencias Exact. Fis. Nat. Madrid
- Pub Date:
- April 2018
- DOI:
- arXiv:
- arXiv:1701.06640
- Bibcode:
- 2018RvMad.112..555S
- Keywords:
-
- Singular function;
- Fractal;
- Self-similar set;
- Hausdorff–Besicovitch dimension;
- Minkowski function;
- 28A80;
- 26A30;
- 11K55;
- 03E99;
- 11K50;
- Mathematics - Classical Analysis and ODEs
- E-Print:
- 6 pages