三分Cantor集自乘积的Hausdorff测度的估计

贾保国;周作领;朱智伟

数学学报 ›› 2003, Vol. 46 ›› Issue (4) : 747-752.

数学学报 ›› 2003, Vol. 46 ›› Issue (4) : 747-752. DOI: 10.12386/A2003sxxb0100
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三分Cantor集自乘积的Hausdorff测度的估计

    贾保国;周作领;朱智伟
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The Hausdorff Measure of the Cartesian Product of the Middle Third Cantor Set with Itself

    (1)Bao Guo JIA,(2)Zuo Ling ZHO
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摘要

本文证明了三分Cantor集C自乘积集C×C的Hausdorff测度,满足1≤H~((log_3)~4)(C×C)≤1.502879.

Abstract

For the Hausdorff measure of the Cartesian product of the middle third Cantor set with itself, the following estimation 1 ≤ Hlog34(C × C) ≤ 1.502879 has been obtained.

关键词

Hausdorff维数与测度 / Cantor集 / 自相似集

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贾保国;周作领;朱智伟. 三分Cantor集自乘积的Hausdorff测度的估计. 数学学报, 2003, 46(4): 747-752 https://doi.org/10.12386/A2003sxxb0100
(1)Bao Guo JIA,(2)Zuo Ling ZHO. The Hausdorff Measure of the Cartesian Product of the Middle Third Cantor Set with Itself. Acta Mathematica Sinica, Chinese Series, 2003, 46(4): 747-752 https://doi.org/10.12386/A2003sxxb0100

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