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Packing and Hausdorff measures of stable trees [PDF]
, 2010 In this paper we discuss Hausdorff and packing measures of random continuous trees called stable trees. Stable trees form a specific class of L\'evy trees (introduced by Le Gall and Le Jan in 1998) that contains Aldous's continuum random tree (1991 ...
A Berlinkov +35 more
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Generic zero-Hausdorff and one-packing spectral measures [PDF]
Journal of Mathematical Physics, 2021 For some metric spaces of self-adjoint operators, it is shown that the set of operators whose spectral measures have simultaneous zero upper-Hausdorff and one lower-packing dimension contains a dense Gδ subset. Applications include sets of limit-periodic operators.
Silas L. Carvalho, César R. de Oliveira
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On the Fractal Measures and Dimensions of Image Measures on a Class of Moran Sets
Mathematics, 2023 In this work, we focus on the centered Hausdorff measure, the packing measure, and the Hewitt–Stromberg measure that determines the modified lower box dimension Moran fractal sets. The equivalence of these measures for a class of Moran is shown by having
Najmeddine Attia, Bilel Selmi
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ON THE MUTUAL MULTIFRACTAL ANALYSIS FOR SOME NON-REGULAR MORAN MEASURES
Проблемы анализа, 2023 In this paper, we study the mutual multifractal Hausdorff dimension and the packing dimension of level sets 𝐾(𝛼, 𝛽) for some non-regular Moran measures satisfying the so-called Strong Separation Condition.We obtain sufficient conditions for the valid ...
B. Selmi, N. Yu. Svetova
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Classifying Cantor Sets by their Fractal Dimensions [PDF]
, 2010 In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovitch and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-Packing measures, for the family of dimension functions h, and characterize this
Cabrelli, Carlos A. +2 more
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Hausdorff and packing dimension of fibers and graphs of prevalent continuous maps [PDF]
, 2015 The notions of shyness and prevalence generalize the property of being zero and full Haar measure to arbitrary (not necessarily locally compact) Polish groups.
Balka, Richárd +2 more
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Some typical properties of dimensions of sets and measures
Abstract and Applied Analysis, 2005 This paper contains a review of recent results concerning typical properties of dimensions of sets and dimensions of measures. In particular, we are interested in the Hausdorff dimension, box dimension, and packing dimension of sets and in the Hausdorff ...
Józef Myjak
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The packing spectrum for Birkhoff averages on a self-affine repeller [PDF]
, 2010 We consider the multifractal analysis for Birkhoff averages of continuous potentials on a self-affine Sierpi\'{n}ski sponge. In particular, we give a variational principal for the packing dimension of the level sets.
Reeve, Henry WJ
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Sixty Years of Fractal Projections [PDF]
, 2014 Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention.
A. Ferguson +60 more
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Hausdorff and packing measure for thick solenoids [PDF]
Studia Mathematica, 2004 Summary: For a linear solenoid with two different contraction coefficients and box dimension greater than 2, we give precise formulas for the Hausdorff and packing dimensions. We prove that the packing measure is infinite and give a condition necessary and sufficient for the Hausdorff measure to be positive, finite and equivalent to the SBR measure. We
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