Linear functionals and local measures: a version of the riesz representation theorem in the context of metric spaces
The classical version of the Riesz Representation Theorem is proved in the context of localIy compact Hausdorff spaces and the local compactness plays an essential role ([1]). This means, for ins tance, that the theorem is not true when the underlying space is a topological vector space of infinite...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1974 |
| País: | Colombia |
| Institución: | Universidad Nacional de Colombia |
| Repositorio: | Repositorio UN |
| Idioma: | español |
| OAI Identifier: | oai:repositorio.unal.edu.co:unal/42350 |
| Acceso en línea: | https://repositorio.unal.edu.co/handle/unal/42350 http://bdigital.unal.edu.co/32447/ |
| Access Level: | acceso abierto |
| Palabra clave: | Riesz representation compact Hausdorff theorem topological vector space infinite dimension. |
| Sumario: | The classical version of the Riesz Representation Theorem is proved in the context of localIy compact Hausdorff spaces and the local compactness plays an essential role ([1]). This means, for ins tance, that the theorem is not true when the underlying space is a topological vector space of infinite dimension. This paper shows that it is possible to modify the classic proof to establish a natural extension of this theorem in the context of metric spaces or, more generally, in the context on paracomp et spaces (see results in sections 5, 6, 7, 8). |
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