A Decomposition for Borel Measures \(\mu \le \mathcal{H}^{s}\)
| Autor: | Detaille, Antoine, Ponce, Augusto C. |
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| Přispěvatelé: | UCL - SST/IRMP - Institut de recherche en mathématique et physique |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Real Analysis Exchange, Vol. 48, no.1, p. 1-17 (2022) |
| ISSN: | 0147-1937 |
| DOI: | 10.14321/realanalexch.48.1.1629953964 |
| Popis: | We prove that every finite Borel measure $\mu$ in $\mathbb{R}^N$ that is bounded from above by the Hausdorff measure $\mathcal{H}^s$ can be split in countable many parts $\mu\lfloor_{E_k}$ that are bounded from above by the Hausdorff content $\mathcal{H}_\infty^s$. Such a result generalises a theorem due to R. Delaware that says that any Borel set with finite Hausdorff measure can be decomposed as a countable disjoint union of straight sets. We apply this decomposition to show the existence of solutions of a Dirichlet problem involving an exponential nonlinearity. Comment: Added application to solution of semilinear PDE involving exponential |
| Databáze: | OpenAIRE |
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