Visible and invisible cantor sets
In this chapter we study for which Cantor sets there exists a gauge-function h, such that the h−Hausdorff measure—is positive and finite. We show that the collection of sets for which this is true is dense in the set of all compact subsets of a Polish space X. More general, any generic Cantor set sa...
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Springer International Publishing
2013
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| LEADER | 04463caa a22005897a 4500 | ||
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| 001 | PAPER-16756 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518204747.0 | ||
| 008 | 180614s2013 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85047377957 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Cabrelli, C. | |
| 245 | 1 | 0 | |a Visible and invisible cantor sets |
| 260 | |b Springer International Publishing |c 2013 | ||
| 270 | 1 | 0 | |m Molter, U.; Departamento de Matemática FCEyN, Universidad de Buenos Aires, IMAS - CONICETArgentina; email: umolter@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a 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 | ||
| 504 | |a Best, E., A closed dimensionless linear set (1939) Proc. Edinburgh Math. Soc., 2 (6), pp. 105-108 | ||
| 504 | |a Cabrelli, C., Hare, K.E., Molter, U.M., Classifying Cantor sets by their fractal dimensions (2010) Proc. Amer. Math. Soc., 138 (11), pp. 3965-3974 | ||
| 504 | |a Cabrelli, C., Mendivil, F., Molter, U.M., Shonkwiler, R., On the h-Hausdorff measure of Cantor sets (2004) Pac. J. Math., 217, pp. 29-43 | ||
| 504 | |a Davies, R.O., Sets which are null or non-sigma-finite for every translation-invariant measure (1971) Mathematika, 18, pp. 161-162 | ||
| 504 | |a Elekes, M., Keleti, T., Borel sets which are null or non-∏-finite for every translation invariant measure (2006) Adv. Math., 201 (1), pp. 102-115 | ||
| 504 | |a Kechris, A.S., (1995) Descriptive Set Theory, Graduate Texts in Mathematics, Vol. 156, , Springer-Verlag New York | ||
| 504 | |a Rogers, C.A., (1998) Hausdorff Measures, Cambridge Math Library, , Cambridge University Press, Cambridge | ||
| 520 | 3 | |a In this chapter we study for which Cantor sets there exists a gauge-function h, such that the h−Hausdorff measure—is positive and finite. We show that the collection of sets for which this is true is dense in the set of all compact subsets of a Polish space X. More general, any generic Cantor set satisfies that there exists a translation-invariant measure μ for which the set has positive and finite μ-measure.In contrast, we generalize an example of Davies of dimensionless Cantor sets (i.e., a Cantor set for which any translation invariant measure is either 0 or non-σ-finite) that enables us to show that the collection of these sets is also dense in the set of all compact subsets of a Polish space X. © Springer Science+Business Media New York 2013. |l eng | |
| 536 | |a Detalles de la financiación: UL, University of Louisville | ||
| 536 | |a Detalles de la financiación: CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas | ||
| 536 | |a Detalles de la financiación: Acknowledgments C. Cabrelli and U. Molter are partially supported by Grants UBACyT X638 and X502 (UBA) and PIP 112-200801-00398 (CONICET). U. Darji is partially supported by University of Louisville Project Initiation Grant. | ||
| 593 | |a Departamento de Matemática FCEyN, Universidad de Buenos Aires, IMAS - CONICET, C.A.B.A., Argentina | ||
| 593 | |a Department of Mathematics, University of Louisville, Louisville, KY, United States | ||
| 690 | 1 | 0 | |a CANTOR SET |
| 690 | 1 | 0 | |a CANTOR SPACE |
| 690 | 1 | 0 | |a CANTOR TREE |
| 690 | 1 | 0 | |a COMEAGER SET |
| 690 | 1 | 0 | |a DAVIES SET |
| 690 | 1 | 0 | |a DIMENSIONLESS SET |
| 690 | 1 | 0 | |a GENERIC ELEMENT |
| 690 | 1 | 0 | |a HAUSDORFF MEASURE |
| 690 | 1 | 0 | |a POLISH SPACE |
| 690 | 1 | 0 | |a STRONGLY INVISIBLE SET |
| 690 | 1 | 0 | |a TREE |
| 690 | 1 | 0 | |a VISIBLE SET |
| 700 | 1 | |a Darji, U.B. | |
| 700 | 1 | |a Molter, U. | |
| 773 | 0 | |d Springer International Publishing, 2013 |h pp. 11-21 |k n. 9780817683788 |x 22965009 |t Appl. Numer. Harmon. Anal. | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-85047377957&doi=10.1007%2f978-0-8176-8379-5_2&partnerID=40&md5=a219ff8ff82b76a7221264203cd07f39 |y Registro en Scopus |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-0-8176-8379-5_2 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_22965009_v_n9780817683788_p11_Cabrelli |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_22965009_v_n9780817683788_p11_Cabrelli |y Registro en la Biblioteca Digital |
| 961 | |a paper_22965009_v_n9780817683788_p11_Cabrelli |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 77709 | ||