Geodesic
О хаусдорфовой мере однородного треугольного $(c,\theta)$-ковра Серпинского
Problemy analiza, no. 18 (2011), pp. 61-69.

Voir la notice de l'article provenant de la source Math-Net.Ru

The generalized homogeneous Sierpinski $(c,\theta)$-gasket is considered. It has received that the $s$-dimensional Hausdorff measure of $(c, \theta)$-gasket for $c\in (0; 1/3]$ is equal $H^{s}(D_{c,\theta})=(2\sin\frac{\theta}{2})^{s}$, for $\theta\in [\frac{\pi}{3}, \pi)$ and $(\frac{2\sin \theta}{\sqrt{5-4\cos \theta}})^{s}\le H^{s}(D_{c-\theta}) \le 1$ for $\theta\in (0,\frac{\pi}{3})$. As a consequence the $s$-dimensional Hausdorff measure for a generalized homogeneous Pascal triangle is received, it is equal $2^{s/2}$. 
@article{PA_2011_18_a3,
     author = {N. Yu. Svetova},
     title = {{\CYRO} {\cyrh}{\cyra}{\cyru}{\cyrs}{\cyrd}{\cyro}{\cyrr}{\cyrf}{\cyro}{\cyrv}{\cyro}{\cyrishrt} {\cyrm}{\cyre}{\cyrr}{\cyre} {\cyro}{\cyrd}{\cyrn}{\cyro}{\cyrr}{\cyro}{\cyrd}{\cyrn}{\cyro}{\cyrg}{\cyro} {\cyrt}{\cyrr}{\cyre}{\cyru}{\cyrg}{\cyro}{\cyrl}{\cyrsftsn}{\cyrn}{\cyro}{\cyrg}{\cyro} $(c,\theta)$-{\cyrk}{\cyro}{\cyrv}{\cyrr}{\cyra} {{\CYRS}{\cyre}{\cyrr}{\cyrp}{\cyri}{\cyrn}{\cyrs}{\cyrk}{\cyro}{\cyrg}{\cyro}}},
     journal = {Problemy analiza},
     pages = {61--69},
     publisher = {mathdoc},
     number = {18},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PA_2011_18_a3/}
}
TY  - JOUR
AU  - N. Yu. Svetova
TI  - О хаусдорфовой мере однородного треугольного $(c,\theta)$-ковра Серпинского
JO  - Problemy analiza
PY  - 2011
SP  - 61
EP  - 69
IS  - 18
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2011_18_a3/
LA  - ru
ID  - PA_2011_18_a3
ER  - 
%0 Journal Article
%A N. Yu. Svetova
%T О хаусдорфовой мере однородного треугольного $(c,\theta)$-ковра Серпинского
%J Problemy analiza
%D 2011
%P 61-69
%N 18
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2011_18_a3/
%G ru
%F PA_2011_18_a3
N. Yu. Svetova. О хаусдорфовой мере однородного треугольного $(c,\theta)$-ковра Серпинского. Problemy analiza, no. 18 (2011), pp. 61-69. http://geodesic.mathdoc.fr/item/PA_2011_18_a3/

[1] Ayer E., Strichartz R. S., “Exact Hausdorff measure and intervals of maximum density for Cantor sets”, Transactions of the American Mathematical Society, 351:9 (1999), 3725–3741 | DOI | MR | Zbl

[2] Falconer K. J., Fractal geometry. Mathematical Foundations and Applications, John Wiley Sons, New York, 1990, 337 pp. | MR | Zbl

[3] Huojun R., Weiyi S., “An approximation method to estimate the Hausdorff measure of the Sierpinski gasket”, Analysis in Theory and Applications, 20:2 (2004), 158–166 | DOI | MR | Zbl

[4] Jia B., Zhou Z., Zhu Z., “Hausdorff measure of the Sierpinski gasket”, Analysis in Theory and Applications, 22:1 (2006), 8–19 | DOI | MR

[5] Jia B., “Bounds of Hausdorff measure of the Sierpinski gasket”, Journal of Mathematical Analysis and Applications, 330:2 (2007), 1016–1024 | DOI | MR | Zbl

[6] Kreitmeier W., “Hausdorff measure of uniform self-similar fractals”, Analysis in Theory and Applications, 26:1 (2010), 84–100 | DOI | MR | Zbl

[7] Liu D., Dai M., “The Hausdorff measure of the attractor of an iterated function system with parameter”, International Journal of Nonlinear Science, 3:2 (2007), 150–154 | MR

[8] Mora P., “Estimate of the hausdorff measure of the Sierpinski triangle”, Fractals, 2009, no. 2, 137–148 | DOI | MR

[9] Xu S., Su W., Zhou Z., “On the exact Hausdorff measure of a class of self-similar sets satisfying open set condition”, Analysis in Theory and Applications, 24:1 (2008), 93–100 | DOI | MR | Zbl

[10] Zuoling Z., “Hausdorff measure of Sierpinski gasket”, Science in China (Series A), 40:10 (1997), 1016–1021 | DOI | MR | Zbl