三分Cantor集自乘积的Hausdorff测度上限的估计(英文)  

The Hausdorff Measure of the Cartesian Product of the Middle Third Cantor Set with Itself

作　　者：刘娟[1] 许绍元[1] 

机构地区：[1]淮北煤炭师范学院数学系,安徽淮北235000

出　　处：《淮北煤炭师范学院学报（自然科学版）》2006年第1期1-4,共4页Journal of Huaibei Coal Industry Teachers College(Natural Science edition)

基　　金：安徽省教育厅自然科学研究计划项目(2003kj047zd);淮北煤炭师范学院教学研究项目(8088)~~

摘　　要：文章证明了三分Cantor集C的自乘积C×C的Hausdorff测度的上限满足,Hlog34(C×C)1.495901改进了现有文献的有关结果.In this paper we prove that for the Hausdorff measure of the Cartesian product of the middle third Cantor set with itself, the following estimation H^log4（C×C）≤1.495901 has been obtained. As result of it, we improve the corresponding result.

关 键 词：自相似集 HAUSDORFF维数与测度 CANTOR集 

分 类 号：O174.12[理学—数学]