Stratification of the single blow-up set for Radon measures
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911596993839104 |
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| author | De Masi, Luigi |
| author_facet | De Masi, Luigi |
| contents | We show that the set of points where the blow-up, in the sense of Preiss, of a signed Radon measure on $\mathbb{R}^n$ is unique and its invariant subspace has dimension $k$ is $k$-rectifiable. As simple applications, we obtain a rectifiability criterion for signed Radon measures and the extension of a result, due to Mattila, on measures having unique blow-up almost everywhere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stratification of the single blow-up set for Radon measures De Masi, Luigi Functional Analysis 28A75, 28A33, 28C10 We show that the set of points where the blow-up, in the sense of Preiss, of a signed Radon measure on $\mathbb{R}^n$ is unique and its invariant subspace has dimension $k$ is $k$-rectifiable. As simple applications, we obtain a rectifiability criterion for signed Radon measures and the extension of a result, due to Mattila, on measures having unique blow-up almost everywhere. |
| title | Stratification of the single blow-up set for Radon measures |
| topic | Functional Analysis 28A75, 28A33, 28C10 |
| url | https://arxiv.org/abs/2512.20498 |