Artículo
Garcia, I.; Molter, U.; Scotto, R. "Dimension functions of Cantor sets" (2007) Proceedings of the American Mathematical Society. 135(10):3151-3161
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Abstract:
We estimate the packing measure of Cantor sets associated to nonincreasing sequences through their decay. This result, dual to one obtained by Besicovitch and Taylor, allows us to characterize the dimension functions recently found by Cabrelli et al for these sets. © 2007 American Mathematical Society.
Registro:
| Documento: | Artículo |
| Título: | Dimension functions of Cantor sets |
| Autor: | Garcia, I.; Molter, U.; Scotto, R. |
| Filiación: | Departamento de Matemática, Facultad de Ingeniería Química, Universidad Nacional del Litoral, Santa Fe, Argentina Imal Conicet Unl, Argentina Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Capital Federal, Argentina CONICET, Argentina Departamento de Matemática, Universidad Nacional del Litoral, Santa Fe, Argentina |
| Palabras clave: | Cantor sets; Dimension function; Hausdorff dimension; Packing measure |
| Año: | 2007 |
| Volumen: | 135 |
| Número: | 10 |
| Página de inicio: | 3151 |
| Página de fin: | 3161 |
| DOI: | http://dx.doi.org/10.1090/S0002-9939-07-09019-3 |
| Título revista: | Proceedings of the American Mathematical Society |
| Título revista abreviado: | Proc. Am. Math. Soc. |
| ISSN: | 00029939 |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00029939_v135_n10_p3151_Garcia.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v135_n10_p3151_Garcia |
Referencias:
- Best, E., A closed dimensionless linear set (1939) Proc. Edinburgh Math. Soc., 6 (2), pp. 105-108. , MR0001824 1:302f
- Besicovitch, A.S., Taylor, S.J., On the complementary intervals of a linear closed set of zero Lebesgue measure (1954) J. London Math. Soc., 29, pp. 449-459. , MR0064849 16:344d
- Cabrelli, C., Hare, K., Molter, U.M., Some counterexamples for Cantor sets (2002) Unpublished Manuscript, , Vanderbilt
- Cabrelli, C.A., Hare, K.E., Molter, U.M., Sums of Cantor sets (1997) Ergodic Theory Dynam. Systems, 17 (6), pp. 1299-1313. , MR1488319 98k:28009
- Cabrelli, C., Mendivil, F., Molter, U.M., Shonkwiler, R., On the Hausdorff fe-measure of Cantor sets (2004) Pacific J. Math., 217 (1), pp. 45-59. , MR2105765 2005h:28013
- Cabrelli, C., Molter, U., Paulauskas, V., Shonkwiler, R., Hausdorff measure of p-Cantorsets (2004) Real Anal. Exchange, 30 (2), pp. 413-433. , MR2177411 2006g:28012
- Falconer, K., (1997) Techniques in Fractal Geometry, , John Wiley & Sons Ltd., Chichester, MR1449135 99f:28013
- Olsen, L., The exact Hausdorff dimension functions of some Cantor sets (2003) Nonlinearity, 16 (3), pp. 963-970. , MR1975790 2004g:28009
- Rogers, C.A., Hausdorff measures (1998) Cambridge Mathematical Library, , Cambridge University Press, Cambridge, MR1692618 2000b:28009
- Tricot Jr., C., Two definitions of fractional dimension (1982) Math. Proc. Cambridge Philos. Soc., 91 (1), pp. 57-74. , MR633256 84d:28013
- Tricot, C., (1995) Curves and Fractal Dimension, , Springer-Verlag, New York, MR1302173 95i:28005
- Taylor, S.J., Tricot, C., Packing measure, and its evaluation for a Brownian path (1985) Trans. Amer. Math. Soc., 288 (2), pp. 679-699. , MR776398 87a:28002
Citas:
---------- APA ----------
Garcia, I., Molter, U. & Scotto, R. (2007) . Dimension functions of Cantor sets. Proceedings of the American Mathematical Society, 135(10), 3151-3161.http://dx.doi.org/10.1090/S0002-9939-07-09019-3
---------- CHICAGO ----------
Garcia, I., Molter, U., Scotto, R. "Dimension functions of Cantor sets" . Proceedings of the American Mathematical Society 135, no. 10 (2007) : 3151-3161.http://dx.doi.org/10.1090/S0002-9939-07-09019-3
---------- MLA ----------
Garcia, I., Molter, U., Scotto, R. "Dimension functions of Cantor sets" . Proceedings of the American Mathematical Society, vol. 135, no. 10, 2007, pp. 3151-3161.http://dx.doi.org/10.1090/S0002-9939-07-09019-3
---------- VANCOUVER ----------
Garcia, I., Molter, U., Scotto, R. Dimension functions of Cantor sets. Proc. Am. Math. Soc. 2007;135(10):3151-3161.http://dx.doi.org/10.1090/S0002-9939-07-09019-3
