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Estimation of the lower bound of Hausdorff measure of a special self-similar fractal set. (Chinese. English summary) Zbl 1117.28004
The authors study the lower bound of the Hausdorff measure of a special fractal introduced by Falconer using the structural property of the self-similar fractal and the principle of mass distribution. They concretely analyse the relationship between the size of diameters of various measurable sets and the mass distributed on them. At last they get an estimation of the lower bound of the Hausdorff measure, i.e. \(H^s(F)\geq 0.8077580\).
MSC:
28A78 Hausdorff and packing measures
28A80 Fractals
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