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Abstract:

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.

Registro:

Documento: Artículo
Título:The sizes of rearrangements of cantor sets
Autor:Hare, K.E.; Mendivil, F.; Zuberman, L.
Filiación:Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada
Department of Mathematics and Statistics, Acadia University, Wolfville, NS, Canada
Departamento de Matemática, FCEN-UBA, Buenos Aires, Argentina
Palabras clave:Cantor Sets; Cut-Out Set; Dimension Functions; Hausdorff Dimension; Packing Dimension
Año:2013
Volumen:56
Número:2
Página de inicio:354
Página de fin:365
DOI: http://dx.doi.org/10.4153/CMB-2011-167-7
Título revista:Canadian Mathematical Bulletin
Título revista abreviado:Can. Math. Bull.
ISSN:00084395
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00084395_v56_n2_p354_Hare

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Citas:

---------- APA ----------
Hare, K.E., Mendivil, F. & Zuberman, L. (2013) . The sizes of rearrangements of cantor sets. Canadian Mathematical Bulletin, 56(2), 354-365.
http://dx.doi.org/10.4153/CMB-2011-167-7
---------- CHICAGO ----------
Hare, K.E., Mendivil, F., Zuberman, L. "The sizes of rearrangements of cantor sets" . Canadian Mathematical Bulletin 56, no. 2 (2013) : 354-365.
http://dx.doi.org/10.4153/CMB-2011-167-7
---------- MLA ----------
Hare, K.E., Mendivil, F., Zuberman, L. "The sizes of rearrangements of cantor sets" . Canadian Mathematical Bulletin, vol. 56, no. 2, 2013, pp. 354-365.
http://dx.doi.org/10.4153/CMB-2011-167-7
---------- VANCOUVER ----------
Hare, K.E., Mendivil, F., Zuberman, L. The sizes of rearrangements of cantor sets. Can. Math. Bull. 2013;56(2):354-365.
http://dx.doi.org/10.4153/CMB-2011-167-7