Singularity of self-similar measures with respect to Hausdorff measures

Besicoviteh (1941) and Egglestone (1949) analyzed subsets of points of the unit interval with given frequencies in the figures of their base-p expansions. We extend this analysis to self-similar sets, by replacing the frequencies of figures with the frequencies of the generating similitudes. We focu...

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Detalles Bibliográficos
Autores: Morán Cabré, Manuel, Rey Simo, José Manuel
Tipo de recurso: informe técnico
Fecha de publicación:1995
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/64093
Acceso en línea:https://hdl.handle.net/20.500.14352/64093
Access Level:acceso abierto
Palabra clave:Self-similar measures
Hausdorff measures
Econometría (Economía)
5302 Econometría
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spelling Singularity of self-similar measures with respect to Hausdorff measuresMorán Cabré, ManuelRey Simo, José ManuelSelf-similar measuresHausdorff measuresEconometría (Economía)5302 EconometríaBesicoviteh (1941) and Egglestone (1949) analyzed subsets of points of the unit interval with given frequencies in the figures of their base-p expansions. We extend this analysis to self-similar sets, by replacing the frequencies of figures with the frequencies of the generating similitudes. We focus on the interplay among such sets, self-similar measures, and Hausdorff measures. We give a fine-tuned classification of the Hausdorff measures according to the singularity of the self-similar measures with respect to those measures. We show that the self-similar measures are concentrated on sets whose frequencies of similitudes obey the law of the iterated logarithmFacultad de Ciencias Económicas y Empresariales. DecanatoUniversidad Complutense de Madrid19951995-01-0119951995-01-01technical reporthttp://purl.org/coar/resource_type/c_18ghinfo:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/20.500.14352/64093reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Atribución-NoComercial-CompartirIgual 3.0 Españahttps://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/640932026-06-02T12:44:21Z
dc.title.none.fl_str_mv Singularity of self-similar measures with respect to Hausdorff measures
title Singularity of self-similar measures with respect to Hausdorff measures
spellingShingle Singularity of self-similar measures with respect to Hausdorff measures
Morán Cabré, Manuel
Self-similar measures
Hausdorff measures
Econometría (Economía)
5302 Econometría
title_short Singularity of self-similar measures with respect to Hausdorff measures
title_full Singularity of self-similar measures with respect to Hausdorff measures
title_fullStr Singularity of self-similar measures with respect to Hausdorff measures
title_full_unstemmed Singularity of self-similar measures with respect to Hausdorff measures
title_sort Singularity of self-similar measures with respect to Hausdorff measures
dc.creator.none.fl_str_mv Morán Cabré, Manuel
Rey Simo, José Manuel
author Morán Cabré, Manuel
author_facet Morán Cabré, Manuel
Rey Simo, José Manuel
author_role author
author2 Rey Simo, José Manuel
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv Self-similar measures
Hausdorff measures
Econometría (Economía)
5302 Econometría
topic Self-similar measures
Hausdorff measures
Econometría (Economía)
5302 Econometría
description Besicoviteh (1941) and Egglestone (1949) analyzed subsets of points of the unit interval with given frequencies in the figures of their base-p expansions. We extend this analysis to self-similar sets, by replacing the frequencies of figures with the frequencies of the generating similitudes. We focus on the interplay among such sets, self-similar measures, and Hausdorff measures. We give a fine-tuned classification of the Hausdorff measures according to the singularity of the self-similar measures with respect to those measures. We show that the self-similar measures are concentrated on sets whose frequencies of similitudes obey the law of the iterated logarithm
publishDate 1995
dc.date.none.fl_str_mv 1995
1995-01-01
1995
1995-01-01
dc.type.none.fl_str_mv technical report
http://purl.org/coar/resource_type/c_18gh
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/64093
url https://hdl.handle.net/20.500.14352/64093
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución-NoComercial-CompartirIgual 3.0 España
https://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución-NoComercial-CompartirIgual 3.0 España
https://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Facultad de Ciencias Económicas y Empresariales. Decanato
publisher.none.fl_str_mv Facultad de Ciencias Económicas y Empresariales. Decanato
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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