s-集的H^s-几乎处处覆盖与Hausdorff测度  

The H^s_ a.e. Coverings and Hausdorff Measures for the s- Sets

作　　者：许绍元[1] 

机构地区：[1]中山大学数学与计算科学学院,广东广州510275

出　　处：《中山大学学报（自然科学版）》2005年第1期121-123,共3页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：安徽省教育厅重点科研资助项目(2003kj047zd)

摘　　要：研究了比自相似集更广泛的一类分形集———s＿集。利用Vitali覆盖定理得到了由Hs＿几乎处处覆盖所描述的s＿集的Hausdorff测度的一个基本性质;作为应用,得到了s＿集的Hausdorff测度与Hausdorff容度相等的充分必要条件。此外,还给出了s＿集存在最好Hs＿几乎处处覆盖的一个充分条件。The s_sets are studied. By using the Vitali Covering Theorem, a basic property describing the Hausdorff measure of the s_set by the notation of H^s_ a\^e\^ covering is obtained. As applications, some sufficient and necessary conditions under which the Hausdorff measure of the s_set equals its Hausdorff content are obtained. In addition, a sufficient condition under which the s_set has an H^s_ a\^e\^ covering is obtained.

关 键 词：s-集与自相似集 HAUSDORFF测度与维数 (最好)H^s-几乎处处覆盖 上凸密度 

分 类 号：O189.1[理学—数学]