Results 171 to 180 of about 5,104 (219)

Hausdorff and packing measure for solenoids

Ergodic Theory and Dynamical Systems, 2003
Summary: We prove that the solenoid with two different contraction coefficients has zero Hausdorff and positive packing measure in its own dimension and the SBR measure is equivalent to the packing measure on the attractor. Further, we prove similar statements for Slanting Baker maps with intersecting cylinders (in \(\mathbb{R}^{2}\)).
Rams, Michał, Simon, Károly
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Hausdorff measures on the Wiener space

Potential Analysis, 1992
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Feyel, D., de La Pradelle, A.
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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 DIMENSION AND HAUSDORFF MEASURES OF JULIA SETS OF ELLIPTIC FUNCTIONS

Bulletin of the London Mathematical Society, 2003
Let \(f: \mathbb{C}\to\overline{\mathbb{C}}\) be an elliptic function and \(q\) be the maximal multiplicity of all poles of \(f\). The authors prove that the Hausdorff dimension of the Julia set of \(f\) is greater than \({2q\over q+1}\), and the Hausdorff dimension of the set of points escaping to infinity is less than or equal to \({2q\over q+1 ...
Kotus, Janina, Urbański, Mariusz
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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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A Characteristic Property of Hausdorff Measure

Journal of the London Mathematical Society, 1950
Man bezeichne mit \(h(x)\) eine für \(x\ge 0\) definierte, stetige, streng wachsende Funktion mit \(h(0) = 0\) und \(\displaystyle\varliminf_{x\to +0} h(\alpha x)/h(x) > 0\) \((0 < \alpha < 1)\). Ist ein separabler, metrischer Raum \(X\) gegeben, so definiert man für \(E\subset X\) \(\text{h. m. }E = \displaystyle\lim_{\delta\to 0} \Lambda_h(E, \delta)\
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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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Hausdorff and Radon Measures

2011
In this chapter we present the fundamental theorems of measure theory, such as the Lebesgue–Besicovitch differentiation theorem, the Stieltjes– Lebesgue theory of integral, the fundamental properties of Hausdorff measures and the general area and coarea formulas.
Mariano Giaquinta, Giuseppe Modica
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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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The Hausdorff measure of non hyperconvexity

1999
A metric space \(X\) is said to be hyperconvex if for every metric space \(Y\) every nonexpansive map from a subset \(S\subseteq Y\) to \(X\) can be extended to a nonexpansive map from \(Y\) to \(X\). A function \(f\in C(X)\) on a metric space \((X,d)\) is called a metric form if for all \(x,y\in X\), \(f(x)+ f(y)\geq d(x,y)\).
CIANCIARUSO, Filomena, DE PASCALE
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