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...
- Autores:
-
Álvarez, Jairo
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1974
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- 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/
- Palabra clave:
- Riesz representation
compact Hausdorff
theorem
topological vector space
infinite dimension.
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | 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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