Artículo
Cabrelli, C.; Molter, U.; Paulauskas, V.; Shonkwiler, R. "Hausdorff measure of p-Cantor sets" (2004) Real Analysis Exchange. 30(2):413-434
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Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | Hausdorff measure of p-Cantor sets |
| Autor: | Cabrelli, C.; Molter, U.; Paulauskas, V.; Shonkwiler, R. |
| Filiación: | Departamento de Matemática, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires and CONICET, Pabellón I - Ciudad Universitaria, Buenor Aires, 1428, Argentina Department of Mathematics and Informatics, Vilnius University, Lithuania Institute of Mathematics and Informatics, Vilnius, Lithuania School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, United States |
| Palabras clave: | Cantor like sets; Hausdorff dimension; Hausdorff measure |
| Año: | 2004 |
| Volumen: | 30 |
| Número: | 2 |
| Página de inicio: | 413 |
| Página de fin: | 434 |
| Título revista: | Real Analysis Exchange |
| Título revista abreviado: | Real Anal. Exch. |
| ISSN: | 01471937 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01471937_v30_n2_p413_Cabrelli |
Referencias:
- Beardon, A.F., On the Hausdorff dimension of general Cantor sets (1965) Proc. Camb. Phil. Soc, 61, pp. 679-694
- Davydov, Y., Paulauskas, V., Račkauskas, A., More on P-Stable Convex Sets in Banach Space (2000) J. of Theor. Probab., 13, No, 1, pp. 39-64
- Falconer, K., (1985) The Geometry of Fractal Sets, , Cambridge University Press
- Falconer, K., (1997) Techniques in Fractal Geometry, , John Wiley & Sons
- Mattila, P., (1995) Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability, 44. , Cambridge Studies in Advanced Mathematics, Cambridge University Press
- Rogers, C.A., (1998) Hausdorff measures, , second ed., Cambridge University Press, Cambridge, UK
- Tsuji, M., On the capacity of general Cantor sets (1953) J. Math. Soc. Japan, 5, pp. 235-252
Citas:
---------- APA ----------
Cabrelli, C., Molter, U., Paulauskas, V. & Shonkwiler, R. (2004) . Hausdorff measure of p-Cantor sets. Real Analysis Exchange, 30(2), 413-434.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01471937_v30_n2_p413_Cabrelli [ ]
---------- CHICAGO ----------
Cabrelli, C., Molter, U., Paulauskas, V., Shonkwiler, R. "Hausdorff measure of p-Cantor sets" . Real Analysis Exchange 30, no. 2 (2004) : 413-434.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01471937_v30_n2_p413_Cabrelli [ ]
---------- MLA ----------
Cabrelli, C., Molter, U., Paulauskas, V., Shonkwiler, R. "Hausdorff measure of p-Cantor sets" . Real Analysis Exchange, vol. 30, no. 2, 2004, pp. 413-434.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01471937_v30_n2_p413_Cabrelli [ ]
---------- VANCOUVER ----------
Cabrelli, C., Molter, U., Paulauskas, V., Shonkwiler, R. Hausdorff measure of p-Cantor sets. Real Anal. Exch. 2004;30(2):413-434.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01471937_v30_n2_p413_Cabrelli [ ]
