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February 2007 The Hausdorff measure of a Sierpinski-like fractal
Ming-Hua WANG
Hokkaido Math. J. 36(1): 9-19 (February 2007). DOI: 10.14492/hokmj/1285766665

Abstract

Let $S$ be a Sierpinski-like fractal with the compression ratio $\frac{1}{3}$, $N$ be the set of all the basic triangles to generate $S$. In this paper, by the mass distribution principle, the exact value of the Hausdorff measure of $S$, $H(S)=1$, is obtained, and the fact that the Hausdorff measure of $S$ can be determined by the net measure $H_N(S)$ is shown, and the best coverings of $S$ that are nontrivial are also obtained.

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Ming-Hua WANG. "The Hausdorff measure of a Sierpinski-like fractal." Hokkaido Math. J. 36 (1) 9 - 19, February 2007. https://doi.org/10.14492/hokmj/1285766665

Information

Published: February 2007
First available in Project Euclid: 29 September 2010

zbMATH: 1157.28304
MathSciNet: MR2309820
Digital Object Identifier: 10.14492/hokmj/1285766665

Subjects:
Primary: 28A80
Secondary: 28A78

Keywords: Hausdorff measure , mass distribution principle , self-similar set , Sierpinski-like fractal

Rights: Copyright © 2007 Hokkaido University, Department of Mathematics

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