The sizes of rearrangements of cantor sets

A linear Cantor setC with zero Lebesgue measure is associated with the countable collection of the bounded complementary open intervals. A rearrangment of C has the same lengths of its complementary intervals, but with different locations. We study the Hausdorff and packing h-measures and dimensiona...

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Autores principales: Hare, K.E., Mendivil, F., Zuberman, L.
Formato: JOUR
Materias:
Cantor Sets
Cut-Out Set
Dimension Functions
Hausdorff Dimension
Packing Dimension
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00084395_v56_n2_p354_Hare
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00084395_v56_n2_p354_Hare2023-10-03T14:06:08Z The sizes of rearrangements of cantor sets Hare, K.E. Mendivil, F. Zuberman, L. Cantor Sets Cut-Out Set Dimension Functions Hausdorff Dimension Packing Dimension A linear Cantor setC with zero Lebesgue measure is associated with the countable collection of the bounded complementary open intervals. A rearrangment of C has the same lengths of its complementary intervals, but with different locations. We study the Hausdorff and packing h-measures and dimensional properties of the set of all rearrangments of some given C for general dimension functions h. For each set of complementary lengths, we construct a Cantor set rearrangement which has the maximal Hausdorff and the minimal packing h-premeasure, up to a constant. We also show that if the packing measure of this Cantor set is positive, then there is a rearrangement which has infinite packing measure. © Canadian Mathematical Society 2011. Fil:Zuberman, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00084395_v56_n2_p354_Hare
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 Sets
Cut-Out Set
Dimension Functions
Hausdorff Dimension
Packing Dimension
spellingShingle Cantor Sets
Cut-Out Set
Dimension Functions
Hausdorff Dimension
Packing Dimension
Hare, K.E.
Mendivil, F.
Zuberman, L.
The sizes of rearrangements of cantor sets
topic_facet Cantor Sets
Cut-Out Set
Dimension Functions
Hausdorff Dimension
Packing Dimension
description A linear Cantor setC with zero Lebesgue measure is associated with the countable collection of the bounded complementary open intervals. A rearrangment of C has the same lengths of its complementary intervals, but with different locations. We study the Hausdorff and packing h-measures and dimensional properties of the set of all rearrangments of some given C for general dimension functions h. For each set of complementary lengths, we construct a Cantor set rearrangement which has the maximal Hausdorff and the minimal packing h-premeasure, up to a constant. We also show that if the packing measure of this Cantor set is positive, then there is a rearrangement which has infinite packing measure. © Canadian Mathematical Society 2011.
format JOUR
author Hare, K.E.
Mendivil, F.
Zuberman, L.
author_facet Hare, K.E.
Mendivil, F.
Zuberman, L.
author_sort Hare, K.E.
title The sizes of rearrangements of cantor sets
title_short The sizes of rearrangements of cantor sets
title_full The sizes of rearrangements of cantor sets
title_fullStr The sizes of rearrangements of cantor sets
title_full_unstemmed The sizes of rearrangements of cantor sets
title_sort sizes of rearrangements of cantor sets
url http://hdl.handle.net/20.500.12110/paper_00084395_v56_n2_p354_Hare
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AT hareke sizesofrearrangementsofcantorsets
AT mendivilf sizesofrearrangementsofcantorsets
AT zubermanl sizesofrearrangementsofcantorsets
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