On the hausdorff h-measure of cantor sets

We estimate the Hausdorff measure and dimension of Cantor sets in terms of a sequence given by the lengths of the bounded complementary intervals. The results provide the relation between the decay rate of this sequence and the dimension of the associated Cantor set. It is well-known that not every...

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Detalles Bibliográficos
Autores principales: Cabrelli, C., Mendivil, F., Molter, U.M., Shonkwiler, R.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00308730_v217_n1_p45_Cabrelli
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00308730_v217_n1_p45_Cabrelli
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spelling todo:paper_00308730_v217_n1_p45_Cabrelli2023-10-03T14:40:46Z On the hausdorff h-measure of cantor sets Cabrelli, C. Mendivil, F. Molter, U.M. Shonkwiler, R. We estimate the Hausdorff measure and dimension of Cantor sets in terms of a sequence given by the lengths of the bounded complementary intervals. The results provide the relation between the decay rate of this sequence and the dimension of the associated Cantor set. It is well-known that not every Cantor set on the line is an s-set for some 0 ≤ s ≤ 1. However, if the sequence associated to the Cantor set C is nonincreasing, we show that C is an h-set for some continuous, concave dimension function h. We construct the function h from the sequence associated to the set C. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00308730_v217_n1_p45_Cabrelli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We estimate the Hausdorff measure and dimension of Cantor sets in terms of a sequence given by the lengths of the bounded complementary intervals. The results provide the relation between the decay rate of this sequence and the dimension of the associated Cantor set. It is well-known that not every Cantor set on the line is an s-set for some 0 ≤ s ≤ 1. However, if the sequence associated to the Cantor set C is nonincreasing, we show that C is an h-set for some continuous, concave dimension function h. We construct the function h from the sequence associated to the set C.
format JOUR
author Cabrelli, C.
Mendivil, F.
Molter, U.M.
Shonkwiler, R.
spellingShingle Cabrelli, C.
Mendivil, F.
Molter, U.M.
Shonkwiler, R.
On the hausdorff h-measure of cantor sets
author_facet Cabrelli, C.
Mendivil, F.
Molter, U.M.
Shonkwiler, R.
author_sort Cabrelli, C.
title On the hausdorff h-measure of cantor sets
title_short On the hausdorff h-measure of cantor sets
title_full On the hausdorff h-measure of cantor sets
title_fullStr On the hausdorff h-measure of cantor sets
title_full_unstemmed On the hausdorff h-measure of cantor sets
title_sort on the hausdorff h-measure of cantor sets
url http://hdl.handle.net/20.500.12110/paper_00308730_v217_n1_p45_Cabrelli
work_keys_str_mv AT cabrellic onthehausdorffhmeasureofcantorsets
AT mendivilf onthehausdorffhmeasureofcantorsets
AT molterum onthehausdorffhmeasureofcantorsets
AT shonkwilerr onthehausdorffhmeasureofcantorsets
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