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...
| Authors: | ; |
|---|---|
| Format: | Report |
| Publication date: | 1995 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/64093 |
| Online Access: | https://hdl.handle.net/20.500.14352/64093 |
| Access Level: | Open access |
| Keyword: | Self-similar measures Hausdorff measures Econometría (Economía) 5302 Econometría |
| _version_ | 1878731352355897344 |
|---|---|
| author | Morán Cabré, Manuel |
| author2 | Rey Simo, José Manuel |
| author2_role | author |
| author_browse | Morán Cabré, Manuel Rey Simo, José Manuel |
| author_facet | Morán Cabré, Manuel Rey Simo, José Manuel |
| author_role | author |
| collection | Docta Complutense |
| 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 |
| eu_rights_str_mv | openAccess |
| format | report |
| id | ES_2ddd5c5fe5fc39054fa0ecb9c92dfd3c |
| institution | Universidad Complutense de Madrid (UCM) |
| instname_str | Universidad Complutense de Madrid (UCM) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:docta.ucm.es:20.500.14352/64093 |
| publishDate | 1995 |
| publishDateSort | 1995 |
| publisher | Facultad de Ciencias Económicas y Empresariales. Decanato |
| publisherStr | Facultad de Ciencias Económicas y Empresariales. Decanato |
| reponame_str | Docta Complutense |
| spelling | Singularity of self-similar measures with respect to Hausdorff measures Morán Cabré, Manuel Rey Simo, José Manuel Self-similar measures Hausdorff measures Econometría (Economía) 5302 Econometría 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 Facultad de Ciencias Económicas y Empresariales. Decanato https://hdl.handle.net/20.500.14352/64093 |
| spellingShingle | Singularity of self-similar measures with respect to Hausdorff measures Morán Cabré, Manuel Self-similar measures Hausdorff measures Econometría (Economía) 5302 Econometría |
| title | 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_short | Singularity of self-similar measures with respect to Hausdorff measures |
| title_sort | Singularity of self-similar measures with respect to Hausdorff measures |
| topic | Self-similar measures Hausdorff measures Econometría (Economía) 5302 Econometría |
| topic_facet | Self-similar measures Hausdorff measures Econometría (Economía) 5302 Econometría |
| url | https://hdl.handle.net/20.500.14352/64093 |