The Lebesgue measure of boundaries of multigeometric Cantorvals
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918171108179968 |
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| author | Nowakowski, Piotr Prus-Wiśniowski, Franciszek |
| author_facet | Nowakowski, Piotr Prus-Wiśniowski, Franciszek |
| contents | 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 $\mathcal{G}_δ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Lebesgue measure of boundaries of multigeometric Cantorvals Nowakowski, Piotr Prus-Wiśniowski, Franciszek Dynamical Systems Classical Analysis and ODEs 40A05, 11B05, 28A75 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 $\mathcal{G}_δ$. |
| title | The Lebesgue measure of boundaries of multigeometric Cantorvals |
| topic | Dynamical Systems Classical Analysis and ODEs 40A05, 11B05, 28A75 |
| url | https://arxiv.org/abs/2510.21878 |