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EnglishWe review some classical differentiation theorems for measures, showing how they can be turned into an integral representation of a Borel measure with respect to a fixed Carathe'odory measure. We focus our attention on the case this measure is the spherical Hausdorff measure, giving a metric measure area formula. Our point consists in using certain covering derivatives as ``generalized densities''. Some consequences for the sub-Riemannian Heisenberg group are also pointed out.
| Autori interni: | |
| Autori: | Magnani, Valentino |
| Titolo: | On a measure theoretic area formula |
| Anno del prodotto: | 2015 |
| Abstract: | We review some classical differentiation theorems for measures, showing how they can be turned into an integral representation of a Borel measure with respect to a fixed Carathe'odory measure. We focus our attention on the case this measure is the spherical Hausdorff measure, giving a metric measure area formula. Our point consists in using certain covering derivatives as ``generalized densities''. Some consequences for the sub-Riemannian Heisenberg group are also pointed out. |
| Digital Object Identifier (DOI): | 10.1017/S030821051500013X |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| PRSE-M.pdf | Articolo principale | Documento in Post-print |  | Open AccessVisualizza/Apri |
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