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http://dx.doi.org/10.4134/BKMS.2012.49.5.1041

THE PARAMETER DISTRIBUTION SET FOR A SELF-SIMILAR MEASURE  

Baek, In-Soo (Department of Mathematics Pusan University of Foreign Studies)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.5, 2012 , pp. 1041-1055 More about this Journal
Abstract
The parameter lower (upper) distribution set corresponds to the cylindrical lower or upper local dimension set for a self-similarmeasure on a self-similar set satisfying the open set condition.
Keywords
Hausdorff dimension; packing dimension; self-similar set; distribution set; local dimension set;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 A. Schief, Separation properties for self-similar sets, Proc. Amer. Math. Soc. 122 (1994), no. 1, 111-115.   DOI
2 I.-S. Baek, Relation between spectral classes of a self-similar Cantor set, J. Math. Anal. Appl. 292 (2004), no. 1, 294-302.   DOI   ScienceOn
3 I.-S. Baek, Derivative of the Riesz-Nagy -Takacs function, Bull. Korean Math. Soc. 48 (2011), no. 2, 261-275.   DOI   ScienceOn
4 I.-S. Baek, The derivative and moment of the generalized Riesz-Nagy-Takacs function, preprint.
5 I.-S. Baek, L. Olsen, and N. Snigireva, Divergence points of self-similar measures and packing dimension, Adv. Math. 214 (2007), no. 1, 267-287.   DOI   ScienceOn
6 R. Cawley and R. D. Mauldin, Multifractal decompositions of Moran fractals, Adv. Math. 92 (1992), no. 2, 196-236.   DOI
7 G. A. Edgar, Measure, Topology, and Fractal Geometry, Springer Verlag, 1990.
8 M. Elekes, T. Keleti, and A. Mathe, Self-similar and self-affine sets; measures of the intersection of two copies, Ergodic Theory Dynam. Systems 30 (2010), no. 2, 399-440.   DOI   ScienceOn
9 K. J. Falconer, Techniques in Fractal Geometry, John Wiley and Sons, 1997.
10 W. Li, An equivalent definition of packing dimension and its application, Nonlinear Anal. Real World Appl. 10 (2009), no. 3, 1618-1626.   DOI   ScienceOn
11 M. Moran, Multifractal components of multiplicative set functions, Math. Nachr. 229 (2001), 129-160.   DOI
12 L. Olsen, A multifractal formalism, Adv. Math. 116 (1995), no. 1, 82-196.   DOI   ScienceOn
13 L. Olsen and S. Winter, Normal and non-normal points of self-similar sets and divergence points of a self-similar measures, J. London Math. Soc. 67 (2003), no. 3, 103-122.   DOI