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On one fractal property of the Minkowski function. (English) Zbl 1387.28013
Summary: 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.

28A80 Fractals
11K50 Metric theory of continued fractions
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
26A30 Singular functions, Cantor functions, functions with other special properties
Full Text: DOI
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