The Hausdorff measure of a Sierpinski-like fractal
WANG, Ming-Hua
Hokkaido Math. J., Tome 36 (2007) no. 4, p. 9-19 / Harvested from Project Euclid
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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.
Publié le : 2007-02-15
Classification:  self-similar set,  Sierpinski-like fractal,  Hausdorff measure,  mass distribution principle,  28A80,  28A78 
@article{1285766665,
     author = {WANG, Ming-Hua},
     title = {The Hausdorff measure of a Sierpinski-like fractal},
     journal = {Hokkaido Math. J.},
     volume = {36},
     number = {4},
     year = {2007},
     pages = { 9-19},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1285766665}
}

WANG, Ming-Hua. The Hausdorff measure of a Sierpinski-like fractal. Hokkaido Math. J., Tome 36 (2007) no. 4, pp.  9-19. http://gdmltest.u-ga.fr/item/1285766665/