Results 251 to 260 of about 72,312 (306)

Scaling Hausdorff measures

Mathematika, 1989
In this note, we investigate those Hausdorff measures which obey a simple scaling law. Consider a continuous increasing function θ defined on with θ(0)= 0 and let be the corresponding Hausdorff measure. We say that obeys an order α scaling law provided whenever K⊂ and c> 0, thenor, equivalently, if T is a similarity map of with similarity ratio c:
R. Daniel Mauldin, S. C. Williams
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Hausdorff measure and linear forms.

Journal für die reine und angewandte Mathematik (Crelles Journal), 1997
It is shown that given any dimension function \(f\), the Hausdorff measure \({\mathcal H}^f\) of the set of well approximable linear forms \(W(m,n; \psi)\) is zero or infinity depending on whether a certain volume sum converges or diverges. This is a Hausdorff measure analogue of the classical Khintchine-Groshev theorem where the \(mn\)-dimensional ...
Dickinson, Detta, Velani, Sanju L.
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Hausdorff Measure of Homogeneous Cantor Set

Acta Mathematica Sinica, English Series, 2001
In this short note, the authors give an exact expression of the Hausdorff measure of a class of homogeneous Cantor sets refining the results of \textit{D. J. Feng}, \textit{H. Rao} and \textit{J. Wu} [Progr. Nat. Sci. 6, 673-678 (1996) (per bibl.)] and \textit{D. J. Feng}, \textit{Z. Y. Wen} and \textit{J. Wu} [Sci. China, Ser. A 40, No.
Qu, Cheng Qin, Rao, Hui, Su, Wei Yi
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Hausdorff measure of Sierpinski gasket

Science in China Series A: Mathematics, 1997
The author gives a new estimate on the upper bound of the Hausdorff measure of the Sierpiński gasket \(S: H^s(S)\leq{25\over 22}\left({6\over 7}\right)^s\), where \(s= \log_23\) is the Hausdorff dimension of \(S\). The result improves the previous estimates obtained by the author [Proc. Nat. Sci. (English Ed.) 7, No.
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On the Centred Hausdorff Measure

Journal of the London Mathematical Society, 2000
Summary: Let \(\nu\) be a measure on a separable metric space. For \(t,q\in\mathbb{R}\), the centred Hausdorff measure \(\mu^h\) with the gauge function \(h(x,r)= r^t(\nu B(x,r))^q\) is studied. The dimension defined by these measures plays an important role in the study of multifractals. It is shown that if \(\nu\) is a doubling measure, then \(\mu^h\)
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Hausdorff-Gauss Measures

2001
According to a result of Bouleau-Hirsch, the law of an ℝ n -valued Wiener functional belonging to the Gaussian-Dirichlet space W 1,2has a density with respect to Lebesgue measure λn. On the other hand there exists a classical formula for changing variables, the coarea Federer formula for Lipschitz functions.
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Singular measures and Hausdorff measures

Israel Journal of Mathematics, 1969
An example is given of a family of singular probability measures on the unit interval which are supported on a set of fractional Hausdorff dimension but cannot be represented as Hausdorff measures.
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Hausdorff Measure and Local Measure

Journal of the London Mathematical Society, 1982
Johnson, Roy A., Rogers, C. A.
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\(\Gamma\) convergence of Hausdorff measures

2005
Starting from the Golab Theorem, which states that in a metric space \((Q,d)\) the Hausdorff measure \({\mathcal H}^1_d\), when restricted to the class of the compact connected subsets of \(Q\), is lower semicontinuous for the Hausdorff distance between sets, it is shown that actually a more general result holds for the \(\Gamma\)-convergence of ...
BUTTAZZO, GIUSEPPE, B. SCHWEIZER
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