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arXiv · 2510.21878

The Lebesgue measure of boundaries of multigeometric Cantorvals

Piotr Nowakowski·Franciszek Prus-Wiśniowski
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Abstract

We prove that the boundary of every multigeometric Cantorval is a null set, and extend this result to a larger class of standard achievable Cantorvals. In addition, we discuss the sets of uniqueness of achievement sets and show that they always belong to the Borel class $\mathcal{G}_\delta$.

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Piotr Nowakowski, Franciszek Prus-Wiśniowski. 2025-10-23. The Lebesgue measure of boundaries of multigeometric Cantorvals. https://arxiv.org/abs/2510.21878

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