Sets which are not tube null and intersection properties of random measures

Autores
Shmerkin, Pablo Sebastian; Suomala, Ville
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show that in ℝd there are purely unrectifiable sets of Hausdorff (and even box counting) dimension d - 1 which are not tube null, settling a question of Carbery, Soria and Vargas, and improving a number of results by the same authors and by Carbery. Our method extends also to 'convex tube null sets', establishing a contrast with a theorem of Alberti, Csörnyei and Preiss on Lipschitz-null sets. The sets we construct are random, and the proofs depend on intersection properties of certain random fractal measures with curves.
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Suomala, Ville. Universidad de Oulu; Finlandia
Materia
Tube Null
Random Measures
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:11336/38162
Acceder
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spelling Sets which are not tube null and intersection properties of random measuresShmerkin, Pablo SebastianSuomala, VilleTube NullRandom Measureshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We show that in ℝd there are purely unrectifiable sets of Hausdorff (and even box counting) dimension d - 1 which are not tube null, settling a question of Carbery, Soria and Vargas, and improving a number of results by the same authors and by Carbery. Our method extends also to 'convex tube null sets', establishing a contrast with a theorem of Alberti, Csörnyei and Preiss on Lipschitz-null sets. The sets we construct are random, and the proofs depend on intersection properties of certain random fractal measures with curves.Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Suomala, Ville. Universidad de Oulu; FinlandiaOxford University Press2015-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/38162Shmerkin, Pablo Sebastian; Suomala, Ville; Sets which are not tube null and intersection properties of random measures; Oxford University Press; Journal of the London Mathematical Society; 91; 2; 2-2015; 405-4220024-61071469-7750CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1112/jlms/jdu083/abstractinfo:eu-repo/semantics/altIdentifier/doi/10.1112/jlms/jdu083info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:32:51Zoai:ri.conicet.gov.ar:11336/38162instacron: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:34982025-11-12 09:32:51.6CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Sets which are not tube null and intersection properties of random measures
title Sets which are not tube null and intersection properties of random measures
spellingShingle Sets which are not tube null and intersection properties of random measures
Shmerkin, Pablo Sebastian
Tube Null
Random Measures
title_short Sets which are not tube null and intersection properties of random measures
title_full Sets which are not tube null and intersection properties of random measures
title_fullStr Sets which are not tube null and intersection properties of random measures
title_full_unstemmed Sets which are not tube null and intersection properties of random measures
title_sort Sets which are not tube null and intersection properties of random measures
dc.creator.none.fl_str_mv Shmerkin, Pablo Sebastian
Suomala, Ville
author Shmerkin, Pablo Sebastian
author_facet Shmerkin, Pablo Sebastian
Suomala, Ville
author_role author
author2 Suomala, Ville
author2_role author
dc.subject.none.fl_str_mv Tube Null
Random Measures
topic Tube Null
Random Measures
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We show that in ℝd there are purely unrectifiable sets of Hausdorff (and even box counting) dimension d - 1 which are not tube null, settling a question of Carbery, Soria and Vargas, and improving a number of results by the same authors and by Carbery. Our method extends also to 'convex tube null sets', establishing a contrast with a theorem of Alberti, Csörnyei and Preiss on Lipschitz-null sets. The sets we construct are random, and the proofs depend on intersection properties of certain random fractal measures with curves.
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Suomala, Ville. Universidad de Oulu; Finlandia
description We show that in ℝd there are purely unrectifiable sets of Hausdorff (and even box counting) dimension d - 1 which are not tube null, settling a question of Carbery, Soria and Vargas, and improving a number of results by the same authors and by Carbery. Our method extends also to 'convex tube null sets', establishing a contrast with a theorem of Alberti, Csörnyei and Preiss on Lipschitz-null sets. The sets we construct are random, and the proofs depend on intersection properties of certain random fractal measures with curves.
publishDate 2015
dc.date.none.fl_str_mv 2015-02
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/11336/38162
Shmerkin, Pablo Sebastian; Suomala, Ville; Sets which are not tube null and intersection properties of random measures; Oxford University Press; Journal of the London Mathematical Society; 91; 2; 2-2015; 405-422
0024-6107
1469-7750
CONICET Digital
CONICET
url http://hdl.handle.net/11336/38162
identifier_str_mv Shmerkin, Pablo Sebastian; Suomala, Ville; Sets which are not tube null and intersection properties of random measures; Oxford University Press; Journal of the London Mathematical Society; 91; 2; 2-2015; 405-422
0024-6107
1469-7750
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1112/jlms/jdu083/abstract
info:eu-repo/semantics/altIdentifier/doi/10.1112/jlms/jdu083
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 Oxford University Press
publisher.none.fl_str_mv Oxford University Press
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 13.25334

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