Marstrand's density theorem for arbitrary norms in the plane
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866908497098047488 |
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| author | Del Nin, Giacomo Merlo, Andrea |
| author_facet | Del Nin, Giacomo Merlo, Andrea |
| contents | We show that if a non-trivial measure in the plane admits, at almost every point, positive and finite $α$-dimensional density with respect to some norm, then $α$ must be an integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Marstrand's density theorem for arbitrary norms in the plane Del Nin, Giacomo Merlo, Andrea Classical Analysis and ODEs Metric Geometry 28A75 (primary), 28A78, 49Q15, 46B20 (secondary) We show that if a non-trivial measure in the plane admits, at almost every point, positive and finite $α$-dimensional density with respect to some norm, then $α$ must be an integer. |
| title | Marstrand's density theorem for arbitrary norms in the plane |
| topic | Classical Analysis and ODEs Metric Geometry 28A75 (primary), 28A78, 49Q15, 46B20 (secondary) |
| url | https://arxiv.org/abs/2508.15400 |