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math.PR2024
On the Lebesgue measure of one generalised set of subsums of geometric series
Oleg Makarchuk, Dmytro Karvatskyi
In the present paper, we study a set that can be treated as a generalised set of subsums for a geometric series. This object was discovered independently in various mathematical as…
math.DS2024
Fractal analysis of Guthrie-Nymann's set and its generalisations
Mykola Pratsiovytyi, Dmytro Karvatskyi
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 represe…