孙青杰,苏维宜.拟相似集的Hausdorff测度的特征[J].数学研究及应用,2000,20(4):605~608 |
拟相似集的Hausdorff测度的特征 |
On the Characterization of the Hausdorff Measure On a Quasi-Self-Similar Set |
投稿时间:1997-06-09 |
DOI:10.3770/j.issn:1000-341X.2000.04.026 |
中文关键词: Hausdorff测度 拟自相似 Hausdorff维数. |
英文关键词:Hausdorff Measure Quasi-self-Similar Hansdorff Dimension. |
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中文摘要: |
Siegfried GRAF在文献[1]中给出了自相似集上的Hausdorff测度(简称H-测度)的特征.John McLaughlin在文献[2]中引入了拟相似集的概念,K.J.Falconer又在文献[3]中讨论了拟相似集上H-测度和维数的性质.本文研究拟相似集上的H-测度的特征,并得出在一定条件下支撑于其上满足一定条件的测度与H-测度的等价性条件. |
英文摘要: |
In [1], the characterization of the Hausdorff measure on a self-similar set was given by siegfried GRFA. The concept of quasi-self-similar was introduced by John McLaughin in [2] and then some properties of the Hausdorff measure and dimension on quasi-self-similar sets were disscussed from[3], K.J.Falconer. In this paper, we studied the characterization of the Hausdonff measure on a quasi-self-similar set and deduced that the Hausdorff measure is equavilent to some kind of measure which satisfied some conditions. |
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