On the dimension of an irrigable measure
Giuseppe Devillanova, Sergio Solimini (2007)
Rendiconti del Seminario Matematico della Università di Padova
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Displaying similar documents to “Khinchin's theorem in k dimensions with prime numerator and denominator”
On the dimension of an irrigable measure
Contracting-on-Average Baker Maps
Michał Rams (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We estimate from above and below the Hausdorff dimension of SRB measure for contracting-on-average baker maps.
Separation conditions on controlled Moran constructions
Antti Käenmäki, Markku Vilppolainen (2008)
Fundamenta Mathematicae
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It is well known that the open set condition and the positivity of the t-dimensional Hausdorff measure are equivalent on self-similar sets, where t is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.
A problem of invariance for Lebesgue measure
James Fickett, Jan Mycielski (1979)
Colloquium Mathematicae
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A further discussion of the Hausdorff dimension in Engel expansions
Lu-ming Shen (2010)
Acta Arithmetica
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New prime gaps between and .
Nyman, Bertil, Nicely, Thomas R. (2003)
Journal of Integer Sequences [electronic only]
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On the Information Dimensions
Józef Myjak, Ryszard Rudnicki (2007)
Bollettino dell'Unione Matematica Italiana
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A relationship between the information dimension and the average dimension of a measure is given. Properties of the average dimension are studied.
On the dimensions of certain incommensurably constructed sets.
Veerman, J.J.P., Stošić, B.D. (2000)
Experimental Mathematics
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Hausdorff Measure of Infinitely Generated Self-Similar Sets.
M. Moran (1996)
Monatshefte für Mathematik
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Invariant sets with zero measure and full Hausdorff dimension.
Barreira, Luis, Schmeling, Jörg (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Two counterexamples concerning Hausdorff dimensions of projections
Roy O. Davies (1979)
Colloquium Mathematicae
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Semicontinuity of dimension and measure for locally scaling fractals
L. B. Jonker, J. J. P. Veerman (2002)
Fundamenta Mathematicae
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The basic question of this paper is: If you consider two iterated function systems close to each other in an appropriate topology, are the dimensions of their respective invariant sets close to each other? It is well known that the Hausdorff dimension (and Lebesgue measure) of the invariant set does not depend continuously on the iterated function system. Our main result is that (with a restriction on the "non-conformality" of the transformations) the Hausdorff dimension is a lower semicontinuous...
On the Hausdorff dimension of ultrametric subsets in ℝⁿ
James R. Lee, Manor Mendel, Mohammad Moharrami (2012)
Fundamenta Mathematicae
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For every ε > 0, any subset of ℝⁿ with Hausdorff dimension larger than (1-ε)n must have ultrametric distortion larger than 1/(4ε).
Harmonic measure of some Cantor type sets.
Batakis, Athanassios (1996)
Annales Academiae Scientiarum Fennicae. Mathematica
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On the Hausdorff dimension of the expressible set of certain sequences
Jaroslav Hančl, Radhakrishnan Nair, Lukáš Novotný, Jan Šustek (2012)
Acta Arithmetica
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On Nikodym-type sets in high dimensions
Themis Mitsis (2004)
Studia Mathematica
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We prove that the complement of a higher-dimensional Nikodym set must have full Hausdorff dimension.
On the Hausdorff dimension of a family of self-similar sets with complicated overlaps
Balázs Bárány (2009)
Fundamenta Mathematicae
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We investigate the properties of the Hausdorff dimension of the attractor of the iterated function system (IFS) {γx,λx,λx+1}. Since two maps have the same fixed point, there are very complicated overlaps, and it is not possible to directly apply known techniques. We give a formula for the Hausdorff dimension of the attractor for Lebesgue almost all parameters (γ,λ), γ < λ. This result only holds for almost all parameters: we find a dense set of parameters (γ,λ) for which the Hausdorff...
On the Relations Between 2D and 3D Fractal Dimensions: Theoretical Approach and Clinical Application in Bone Imaging
H. Akkari, I. Bhouri, P. Dubois, M. H. Bedoui (2008)
Mathematical Modelling of Natural Phenomena
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The inner knowledge of volumes from images is an ancient problem. This question becomes complicated when it concerns quantization, as the case of any measurement and in particular the calculation of fractal dimensions. Trabecular bone tissues have, like many natural elements, an architecture which shows a fractal aspect. Many studies have already been developed according to this approach. The question which arises however is to know to which extent it is possible to get an exact determination...