| s-集的Hs-几乎处处覆盖与Hausdorff测度 |
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| 引用本文： | 许绍元. s-集的Hs-几乎处处覆盖与Hausdorff测度[J]. 中山大学学报(自然科学版), 2005, 44(1): 121-123 |
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| 作者姓名： | 许绍元 |
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| 作者单位： | 中山大学数学与计算科学学院,广东,广州,510275 |
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| 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.
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| 关 键 词： | s-集与自相似集 Hausdorff测度与维数 (最好)Hs-几乎处处覆盖 上凸密度 |
| 文章编号： | 0529-6579(2005)01-0121-03 |
| 修稿时间： | 2004-02-26 |
The Hs- a. e. Coverings and Hausdorff Measures for the s- Sets |
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| XU Shao_yuan. The Hs- a. e. Coverings and Hausdorff Measures for the s- Sets[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2005, 44(1): 121-123 |
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| Authors: | XU Shao_yuan |
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| Abstract: | 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. |
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| Keywords: | s_sets and self_similar sets Hausdorff measures and dimensions (best)H~s_ a^e^ coverings upper convex density |
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