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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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
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Álvarez, Jairo79775a03-7f7a-4df7-8a24-4b8bd3c57fc33002019-06-28T10:44:58Z2019-06-28T10:44:58Z1974https://repositorio.unal.edu.co/handle/unal/42350http://bdigital.unal.edu.co/32447/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).application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/31972Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 8, núm. 1 (1974); 15-27 0034-7426Álvarez, Jairo (1974) Linear functionals and local measures: a version of the riesz representation theorem in the context of metric spaces. Revista Colombiana de Matemáticas; Vol. 8, núm. 1 (1974); 15-27 0034-7426 .Linear functionals and local measures: a version of the riesz representation theorem in the context of metric spacesArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTRiesz representationcompact Hausdorfftheoremtopological vector spaceinfinite dimension.ORIGINAL31972-117162-1-PB.pdfapplication/pdf3644913https://repositorio.unal.edu.co/bitstream/unal/42350/1/31972-117162-1-PB.pdf9d239aa9b16ad6cadae965823180e607MD51THUMBNAIL31972-117162-1-PB.pdf.jpg31972-117162-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg7405https://repositorio.unal.edu.co/bitstream/unal/42350/2/31972-117162-1-PB.pdf.jpg39f7b63b6d4dcc6b3187a203a3341cacMD52unal/42350oai:repositorio.unal.edu.co:unal/423502023-02-07 23:05:28.568Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Linear functionals and local measures: a version of the riesz representation theorem in the context of metric spaces
title Linear functionals and local measures: a version of the riesz representation theorem in the context of metric spaces
spellingShingle Linear functionals and local measures: a version of the riesz representation theorem in the context of metric spaces
Riesz representation
compact Hausdorff
theorem
topological vector space
infinite dimension.
title_short Linear functionals and local measures: a version of the riesz representation theorem in the context of metric spaces
title_full Linear functionals and local measures: a version of the riesz representation theorem in the context of metric spaces
title_fullStr Linear functionals and local measures: a version of the riesz representation theorem in the context of metric spaces
title_full_unstemmed Linear functionals and local measures: a version of the riesz representation theorem in the context of metric spaces
title_sort Linear functionals and local measures: a version of the riesz representation theorem in the context of metric spaces
dc.creator.fl_str_mv Álvarez, Jairo
dc.contributor.author.spa.fl_str_mv Álvarez, Jairo
dc.subject.proposal.spa.fl_str_mv Riesz representation
compact Hausdorff
theorem
topological vector space
infinite dimension.
topic Riesz representation
compact Hausdorff
theorem
topological vector space
infinite dimension.
description 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).
publishDate 1974
dc.date.issued.spa.fl_str_mv 1974
dc.date.accessioned.spa.fl_str_mv 2019-06-28T10:44:58Z
dc.date.available.spa.fl_str_mv 2019-06-28T10:44:58Z
dc.type.spa.fl_str_mv Artículo de revista
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url https://repositorio.unal.edu.co/handle/unal/42350
http://bdigital.unal.edu.co/32447/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv http://revistas.unal.edu.co/index.php/recolma/article/view/31972
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
Revista Colombiana de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv Revista Colombiana de Matemáticas; Vol. 8, núm. 1 (1974); 15-27 0034-7426
dc.relation.references.spa.fl_str_mv Álvarez, Jairo (1974) Linear functionals and local measures: a version of the riesz representation theorem in the context of metric spaces. Revista Colombiana de Matemáticas; Vol. 8, núm. 1 (1974); 15-27 0034-7426 .
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
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dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
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dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
institution Universidad Nacional de Colombia
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