Classifying cantor sets by their fractal dimensions

Proceedings of the American Mathematical Society

Volumn 138, Issue 11, 2010, Pages 3965-3974

  Cabrelli, Carlos A ^a   Hare, Kathryn E ^b   Molter, Ursula M ^a  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Cantor set; Cut out set; Hausdorff dimension; Packing dimension

Indexed keywords

EID: 78149248757     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-2010-10396-9     Document Type: Article

References (8)

1. A.S. Besicovitch and S.J. Taylor, On the complementary intervals of a linear closed set of zero Lebesgue measure, J. London Math. Soc. 29(1954), 449-459. MR0064849 (16:344d)
2. C. Cabrelli, F. Mendivil, U. Molter and R. Shonkwiler, On the h-Hausdorff measure of Cantor sets, Pac. J. of Math. 217(2004), 29-43. MR2105765 (2005h:28013)
3. C. Cabrelli, U. Molter, V. Paulauskas and R. Shonkwiler, The Hausdorff dimension of p- Cantor sets, Real Anal. Exchange 30(2004/2005), no.2, 413-433. MR2177411 (2006g:28012)
4. K. Falconer, Techniques in fractal geometry, Wiley and Sons, Chichester, 1997. MR1449135 (99f:28013)
5. I. Garcia, U. Molter and R. Scotto, Dimension functions of Cantor sets, Proc. Amer. Math. Soc. 135(2007), 3151-3161. MR2322745 (2008i:28004)
6. C. A. Rogers, Hausdorff measures, Cambridge Math Library, Cambridge University Press, Cambridge, 1998. MR1692618 (2000b:28009)
7. C. Tricot, Two definitions of fractional dimension, Math. Proc. Camb. Phil. Soc. 91(1982), 57-74. MR633256 (84d:28013)
8. S. J. Taylor and C. Tricot, Packing measure and its evaluation for a Brownian path, Trans. Amer. Math. Soc. 288(1985), 679-699. MR776398 (87a:28002)