Note on packing and weak-packing measures with Hausdorff functions
Journal of Mathematical Analysis and Applications, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhi-Ying Wen
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On the Hausdorff and packing measures of typical compact metric spaces [PDF]
Aequationes Mathematicae, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
L Olsen, Olsen L
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Packing and Hausdorff Measures of Cantor Sets Associated with Series [PDF]
Real Analysis Exchange, 2015 We study a generalization of Morán's sum sets, obtaining information about the $h$-Hausdorff and $h$-packing measures of these sets and certain of their subsets.
Kathryn E Hare, Leandro Zuberman
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Exact Hausdorff and Packing measure of certain Cantor sets, not necessarily self-similar or homogeneous [PDF]
Journal of Mathematical Analysis and Applications, 2019 We compute the exact Hausdorff and Packing measures of linear Cantor sets which might not be self similar or homogeneous . The calculation is based on the local behavior of the natural probability measure supported on the sets.
Leandro Zuberman
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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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Hausdorff measures and packing measures of limit sets of CIFSs of generalized complex continued fractions [PDF]
Journal of Difference Equations and Applications, 2020 arXiv admin note: text overlap with arXiv:1810 ...
Hiroki Sumi
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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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Dimension inequalities of multifractal Hausdorff measures and multifractal packing measures
MATHEMATICA SCANDINAVICA, 2000 Given a Borel probability measure \(\mu\) on \({\mathbb R}^n\), the core of multifractal analysis consists of computing the (Hausdorff) dimensional multifractal spectrum of \(\mu\), that is, \[ f_{\mu}(\alpha)=\text{ dim}\left\{x: \alpha_{\mu}(x):= \lim_{r\rightarrow 0}{\log\mu B(x,r)\over \log r}=\alpha\right\}, \] and then establishing whether the ...
L. Olsen
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On interpreting Patterson–Sullivan measures of geometrically finite groups as Hausdorff and packing measures [PDF]
Ergodic Theory and Dynamical Systems, 2015 We provide a new proof of a theorem whose proof was sketched by Sullivan [Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics.Acta Math.149(3–4) (1982), 215–237], namely that if the Poincaré exponent of a geometrically finite Kleinian group$G$is strictly between its minimal and maximal cusp ranks, then ...
Simmons, David
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A note on the generalized Hausdorff and packing measures of product sets in metric space
Mathematical Inequalities & Applications, 2022 Let $μ$ and $ν$ be two Borel probability measures on two separable metric spaces $\X$ and $\Y$ respectively. For $h, g$ be two Hausdorff functions and $q\in \R$, we introduce and investigate the generalized pseudo-packing measure ${\RRR}_μ^{q, h}$ and the weighted generalized packing measure ${\QQQ}_μ^{q, h}$ to give some product inequalities ...
Guedri, Rihab, Attia, Najmeddine
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