Two-Scale Frostman Measures
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911267677011968 |
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| author | Angelini, Nicolas Molter, Ursula |
| author_facet | Angelini, Nicolas Molter, Ursula |
| contents | We establish a unified Frostman-type framework connecting the classical Hausdorff dimension with the family of intermediate dimensions $\dim_θ$ recently introduced by Falconer, Fraser and Kempton. We define a new geometric quantity $\mathcal{D}(E)$ and prove that, under mild assumptions, there exists a family of measures $\{μ_δ\}$ supported on $E$ satisfying two simultaneous decay conditions, corresponding to the Hausdorff and intermediate Frostman inequalities. Such $(δ, s, t)$-Frostman measures allow for a two-scale characterization of the dimension of $E$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-Scale Frostman Measures Angelini, Nicolas Molter, Ursula Classical Analysis and ODEs We establish a unified Frostman-type framework connecting the classical Hausdorff dimension with the family of intermediate dimensions $\dim_θ$ recently introduced by Falconer, Fraser and Kempton. We define a new geometric quantity $\mathcal{D}(E)$ and prove that, under mild assumptions, there exists a family of measures $\{μ_δ\}$ supported on $E$ satisfying two simultaneous decay conditions, corresponding to the Hausdorff and intermediate Frostman inequalities. Such $(δ, s, t)$-Frostman measures allow for a two-scale characterization of the dimension of $E$. |
| title | Two-Scale Frostman Measures |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2511.04302 |