On packing measures and a theorem of Besicovitch

Autores
Garcia, Ignacio Andres; Shmerkin, Pablo
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let Hh be the h-dimensional Hausdorff measure on Rd. Besicovitch showed that if a set E is null for Hh, then it is null for Hg , for some dimension g smaller than h. We prove that this is not true for packing measures. Moreover, we consider the corresponding questions for sets of non-σ-finite packing measure, and for pre-packing measure instead of packing measure.
Fil: Garcia, Ignacio Andres. Universidad Nacional de Mar del Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata; Argentina
Fil: Shmerkin, Pablo. University Of Surrey; Reino Unido
Materia
Packing 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:11336/8253
Acceder
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spelling On packing measures and a theorem of BesicovitchGarcia, Ignacio AndresShmerkin, PabloPacking Measurehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let Hh be the h-dimensional Hausdorff measure on Rd. Besicovitch showed that if a set E is null for Hh, then it is null for Hg , for some dimension g smaller than h. We prove that this is not true for packing measures. Moreover, we consider the corresponding questions for sets of non-σ-finite packing measure, and for pre-packing measure instead of packing measure.Fil: Garcia, Ignacio Andres. Universidad Nacional de Mar del Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Shmerkin, Pablo. University Of Surrey; Reino UnidoAmer Mathematical Soc2014-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/8253Garcia, Ignacio Andres; Shmerkin, Pablo; On packing measures and a theorem of Besicovitch; Amer Mathematical Soc; Proceedings Of The American Mathematical Society; 142; 8; 7-2014; 2661-26690002-9939enginfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2014-142-08/S0002-9939-2014-11962-9/info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1205.6224v1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:38:27Zoai:ri.conicet.gov.ar:11336/8253instacron: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:34982025-09-29 10:38:27.305CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On packing measures and a theorem of Besicovitch
title On packing measures and a theorem of Besicovitch
spellingShingle On packing measures and a theorem of Besicovitch
Garcia, Ignacio Andres
Packing Measure
title_short On packing measures and a theorem of Besicovitch
title_full On packing measures and a theorem of Besicovitch
title_fullStr On packing measures and a theorem of Besicovitch
title_full_unstemmed On packing measures and a theorem of Besicovitch
title_sort On packing measures and a theorem of Besicovitch
dc.creator.none.fl_str_mv Garcia, Ignacio Andres
Shmerkin, Pablo
author Garcia, Ignacio Andres
author_facet Garcia, Ignacio Andres
Shmerkin, Pablo
author_role author
author2 Shmerkin, Pablo
author2_role author
dc.subject.none.fl_str_mv Packing Measure
topic Packing 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 Hh be the h-dimensional Hausdorff measure on Rd. Besicovitch showed that if a set E is null for Hh, then it is null for Hg , for some dimension g smaller than h. We prove that this is not true for packing measures. Moreover, we consider the corresponding questions for sets of non-σ-finite packing measure, and for pre-packing measure instead of packing measure.
Fil: Garcia, Ignacio Andres. Universidad Nacional de Mar del Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata; Argentina
Fil: Shmerkin, Pablo. University Of Surrey; Reino Unido
description Let Hh be the h-dimensional Hausdorff measure on Rd. Besicovitch showed that if a set E is null for Hh, then it is null for Hg , for some dimension g smaller than h. We prove that this is not true for packing measures. Moreover, we consider the corresponding questions for sets of non-σ-finite packing measure, and for pre-packing measure instead of packing measure.
publishDate 2014
dc.date.none.fl_str_mv 2014-07
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/11336/8253
Garcia, Ignacio Andres; Shmerkin, Pablo; On packing measures and a theorem of Besicovitch; Amer Mathematical Soc; Proceedings Of The American Mathematical Society; 142; 8; 7-2014; 2661-2669
0002-9939
url http://hdl.handle.net/11336/8253
identifier_str_mv Garcia, Ignacio Andres; Shmerkin, Pablo; On packing measures and a theorem of Besicovitch; Amer Mathematical Soc; Proceedings Of The American Mathematical Society; 142; 8; 7-2014; 2661-2669
0002-9939
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2014-142-08/S0002-9939-2014-11962-9/
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1205.6224v1
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
dc.publisher.none.fl_str_mv Amer Mathematical Soc
publisher.none.fl_str_mv Amer Mathematical Soc
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 13.070432

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