On s-set in space of homogeneous type

Autores
Carena, Marilina; Toschi, Marisa
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let (X, d, μ) be a space of homogeneous type. We study the relationship between two types of s-sets: relative to a distance and relative to a measure. We find a condition on a closed subset F of X under which F is an s-set relative to the measure μ if and only if F is an s-set relative to δ. Here δ denotes the quasi-distance defined by Macías and Segovia such that (X, δ, μ) is a normal space. In order to prove this result, we prove a covering type lemma and a type of Hausdorff measure based criterion for a given set to be an s-set relative to μ.
Fil: Carena, Marilina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Toschi, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Materia
SPACES OF HOMOGENEOUS TYPE
S-SETS
HAUSDORFF MEASURE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/31885
Acceder
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spelling On s-set in space of homogeneous typeCarena, MarilinaToschi, MarisaSPACES OF HOMOGENEOUS TYPES-SETSHAUSDORFF MEASUREhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let (X, d, μ) be a space of homogeneous type. We study the relationship between two types of s-sets: relative to a distance and relative to a measure. We find a condition on a closed subset F of X under which F is an s-set relative to the measure μ if and only if F is an s-set relative to δ. Here δ denotes the quasi-distance defined by Macías and Segovia such that (X, δ, μ) is a normal space. In order to prove this result, we prove a covering type lemma and a type of Hausdorff measure based criterion for a given set to be an s-set relative to μ.Fil: Carena, Marilina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Toschi, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaPolish Academy of Sciences. Institute of Mathematics2015-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/31885Toschi, Marisa; Carena, Marilina; On s-set in space of homogeneous type; Polish Academy of Sciences. Institute of Mathematics; Colloquium Mathematicum; 138; 2; 1-2015; 193-2030010-1354CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1312.2971info:eu-repo/semantics/altIdentifier/doi/10.4064/cm138-2-4info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:23:07Zoai:ri.conicet.gov.ar:11336/31885instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:23:07.954CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On s-set in space of homogeneous type
title On s-set in space of homogeneous type
spellingShingle On s-set in space of homogeneous type
Carena, Marilina
SPACES OF HOMOGENEOUS TYPE
S-SETS
HAUSDORFF MEASURE
title_short On s-set in space of homogeneous type
title_full On s-set in space of homogeneous type
title_fullStr On s-set in space of homogeneous type
title_full_unstemmed On s-set in space of homogeneous type
title_sort On s-set in space of homogeneous type
dc.creator.none.fl_str_mv Carena, Marilina
Toschi, Marisa
author Carena, Marilina
author_facet Carena, Marilina
Toschi, Marisa
author_role author
author2 Toschi, Marisa
author2_role author
dc.subject.none.fl_str_mv SPACES OF HOMOGENEOUS TYPE
S-SETS
HAUSDORFF MEASURE
topic SPACES OF HOMOGENEOUS TYPE
S-SETS
HAUSDORFF MEASURE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let (X, d, μ) be a space of homogeneous type. We study the relationship between two types of s-sets: relative to a distance and relative to a measure. We find a condition on a closed subset F of X under which F is an s-set relative to the measure μ if and only if F is an s-set relative to δ. Here δ denotes the quasi-distance defined by Macías and Segovia such that (X, δ, μ) is a normal space. In order to prove this result, we prove a covering type lemma and a type of Hausdorff measure based criterion for a given set to be an s-set relative to μ.
Fil: Carena, Marilina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Toschi, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
description Let (X, d, μ) be a space of homogeneous type. We study the relationship between two types of s-sets: relative to a distance and relative to a measure. We find a condition on a closed subset F of X under which F is an s-set relative to the measure μ if and only if F is an s-set relative to δ. Here δ denotes the quasi-distance defined by Macías and Segovia such that (X, δ, μ) is a normal space. In order to prove this result, we prove a covering type lemma and a type of Hausdorff measure based criterion for a given set to be an s-set relative to μ.
publishDate 2015
dc.date.none.fl_str_mv 2015-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/31885
Toschi, Marisa; Carena, Marilina; On s-set in space of homogeneous type; Polish Academy of Sciences. Institute of Mathematics; Colloquium Mathematicum; 138; 2; 1-2015; 193-203
0010-1354
CONICET Digital
CONICET
url http://hdl.handle.net/11336/31885
identifier_str_mv Toschi, Marisa; Carena, Marilina; On s-set in space of homogeneous type; Polish Academy of Sciences. Institute of Mathematics; Colloquium Mathematicum; 138; 2; 1-2015; 193-203
0010-1354
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1312.2971
info:eu-repo/semantics/altIdentifier/doi/10.4064/cm138-2-4
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Polish Academy of Sciences. Institute of Mathematics
publisher.none.fl_str_mv Polish Academy of Sciences. Institute of Mathematics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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