Continuous valuations on the space of Lipschitz functions on the sphere
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere S. After introducing an appropriate notion of convergence, we show that continuous valuations are bounded on sets which are bounded with respect to the Lipschitz norm. This fact, in combination with me...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/231242 |
| Acceso en línea: | http://hdl.handle.net/10261/231242 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometric valuation theory Lipschitz functions integral representation |
| Sumario: | We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere S. After introducing an appropriate notion of convergence, we show that continuous valuations are bounded on sets which are bounded with respect to the Lipschitz norm. This fact, in combination with measure theoretical arguments, will yield an integral representation for continuous and rotation invariant valuations on the space of Lipschitz functions over the 1-dimensional sphere. |
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