摘要
讨论了满足开集条件的自相似集.对于此类分形,用自然覆盖类估计它的Hausdorff测度只能得到一个上限,因而如何判断某一个上限就是它的 Hausdorff测度的准确值是一个重要的问题.本文给出了一个判据.作为应用,统一处理了一类自相似集,得到了平面上的一个Cantor集—Cantor尘的Hausdorff测度的准确值,并重新计算了直线上的Cantor集以及一个 Sierpinski地毯的 Hausdorff测度.
The self-similar sets satisfying the open condition have been studied. An esti- mation of the fractal, by a class of natural covers, can only give the upper limit of its Hausdorff measure. So to judge if such an upper limit is its exact value or not is important. A criterion has been given in this paper. As applications, we have together discussed some self-similar sets, and obtained the exact value of the Hausdorff measure of a Cantor dust.
出处
《数学进展》
CSCD
北大核心
2002年第2期157-162,共6页
Advances in Mathematics(China)
基金
安徽省教育厅自然科学研究项目资助(No.2001kj199zc).