Koch曲线的Hausdorff测度的改进下界估计  

An Improved Lower Bound Estimation for Hausdorff Measure of Koch Curve

作　　者：郭东亮 GUO Dongliang(School of Electronics and Communication Engineering,Sun Yat-sen University,Guangzhou Guangdong 510006)

机构地区：[1]中山大学电子与通信工程学院,广东广州510006

出　　处：《首都师范大学学报（自然科学版）》2020年第3期13-16,共4页Journal of Capital Normal University：Natural Science Edition

基　　金：广东省自然科学基金项目(2018B0303110016)。

摘　　要：为了研究Koch曲线的Hausdorff测度的下界,本文在Koch曲线上定义了质量分布函数μ,对任意覆盖U导出了关系式μ(U)≤1.876|U|s,利用质量分布原理,得到了Koch曲线的Hausdorff测度下界的更好估计值Hs(K)≥0.533049041.The lower bound of Hausdorff measure of Koch curve is studied.The mass distribution functionμis defined on Koch curve.The relationμ(U)≤1.876|U|s for arbitrary coverage U is derived.By using the principle of mass distribution,a better estimate of the lower bound of Hausdorff measure of Koch curve Hs(K)≥0.533049041 is obtained.

关 键 词：KOCH曲线 HAUSDORFF测度 质量分布原理 下界估计 

分 类 号：O174.12[理学—数学]