Hausdorff measure of p-Cantor sets

In this paper we analyze Cantor type sets constructed by the removal of open intervals whose lengths are the terms of the p-sequence, (k-p)k=1 ∞. We prove that these Cantor sets are s-sets, by providing sharp estimates of their Hausdorff measure and dimension. Sets of similar structure arise when st...

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Autores principales: Cabrelli, C., Molter, U., Paulauskas, V., Shonkwiler, R.
Formato: JOUR
Materias:
Cantor like sets
Hausdorff dimension
Hausdorff measure
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01471937_v30_n2_p413_Cabrelli
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_01471937_v30_n2_p413_Cabrelli
record_format dspace
spelling todo:paper_01471937_v30_n2_p413_Cabrelli2023-10-03T15:00:28Z Hausdorff measure of p-Cantor sets Cabrelli, C. Molter, U. Paulauskas, V. Shonkwiler, R. Cantor like sets Hausdorff dimension Hausdorff measure In this paper we analyze Cantor type sets constructed by the removal of open intervals whose lengths are the terms of the p-sequence, (k-p)k=1 ∞. We prove that these Cantor sets are s-sets, by providing sharp estimates of their Hausdorff measure and dimension. Sets of similar structure arise when studying the set of extremal points of the boundaries of the so-called random stable zonotopes. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01471937_v30_n2_p413_Cabrelli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Cantor like sets
Hausdorff dimension
Hausdorff measure
spellingShingle Cantor like sets
Hausdorff dimension
Hausdorff measure
Cabrelli, C.
Molter, U.
Paulauskas, V.
Shonkwiler, R.
Hausdorff measure of p-Cantor sets
topic_facet Cantor like sets
Hausdorff dimension
Hausdorff measure
description In this paper we analyze Cantor type sets constructed by the removal of open intervals whose lengths are the terms of the p-sequence, (k-p)k=1 ∞. We prove that these Cantor sets are s-sets, by providing sharp estimates of their Hausdorff measure and dimension. Sets of similar structure arise when studying the set of extremal points of the boundaries of the so-called random stable zonotopes.
format JOUR
author Cabrelli, C.
Molter, U.
Paulauskas, V.
Shonkwiler, R.
author_facet Cabrelli, C.
Molter, U.
Paulauskas, V.
Shonkwiler, R.
author_sort Cabrelli, C.
title Hausdorff measure of p-Cantor sets
title_short Hausdorff measure of p-Cantor sets
title_full Hausdorff measure of p-Cantor sets
title_fullStr Hausdorff measure of p-Cantor sets
title_full_unstemmed Hausdorff measure of p-Cantor sets
title_sort hausdorff measure of p-cantor sets
url http://hdl.handle.net/20.500.12110/paper_01471937_v30_n2_p413_Cabrelli
work_keys_str_mv AT cabrellic hausdorffmeasureofpcantorsets
AT molteru hausdorffmeasureofpcantorsets
AT paulauskasv hausdorffmeasureofpcantorsets
AT shonkwilerr hausdorffmeasureofpcantorsets
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