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arXiv · 2405.16576

Fractal analysis of Guthrie-Nymann's set and its generalisations

Mykola Pratsiovytyi·Dmytro Karvatskyi
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Abstract

In this paper, we study the fractal properties of the boundary of the Cantorval connected with Guthrie-Nymann's series. In particular, we prove that such a Cantorval can be represented as a union of open intervals and a Cantor set having zero Lebesgue measure and a fractional Hausdorff dimension. Moreover, we extend the result to a countable family of Cantorvals with a similar structure.

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Mykola Pratsiovytyi, Dmytro Karvatskyi. 2024-05-26. Fractal analysis of Guthrie-Nymann's set and its generalisations. https://arxiv.org/abs/2405.16576

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