Results 141 to 150 of about 69,299 (185)

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.
M. Smorodinsky, M. Smorodinsky
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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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A property of Hausdorff measure

Mathematical Proceedings of the Cambridge Philosophical Society, 1956
From the fact that Hausdorffs-dimensional measure is a regular Carathéodory outer measure follows (see Saks (3), ch. II, §§ 6, 8) the standard result:TheoremA.If {En} is any increasing sequence of sets, then∧sEn→ ∧s(ΣEn)as n→ ∞.Since ∧sXis denned (for every setX) as, the problem arises whether for every positive δ and every increasing sequence of sets ...
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The Hausdorff measure of a Sierpinski carpet

Science in China Series A: Mathematics, 1999
This paper deals with the computation and estimation of the Hausdorff measure. Here, the authors obtain the exact value of the Hausdorff measure of a Sierpiński carpet.
Zuoling Zhou, Min Wu
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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 \(\mathbb{R}^{2}\)).
Károly Simon, Michał Rams
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Approximating sequences and Hausdorff measure

Mathematical Proceedings of the Cambridge Philosophical Society, 1974
Approximating sequences have been extensively studied in many branches of mathematics, for example, in number theory (approximating real numbers by rationals) and in numerical analysis (approximations to functions by polynomials). In (1), A. Hyllengren introduced a type of approximating sequence ‘majorizing sequences’ which he used in solving a problem
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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 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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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.
Giuseppe Modica, Mariano Giaquinta
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