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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/38162
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T09:33:02Zoai: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:34982025-09-29 09:33:03.056CONICET 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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1844613012266156032 |
score |
13.070432 |