| 关于自相似集存在最好Hs-几乎处处闭集覆盖的一个新充分必要条件 |
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| 引用本文： | 许绍元.关于自相似集存在最好Hs-几乎处处闭集覆盖的一个新充分必要条件[J].江西师范大学学报(自然科学版),2007,31(3):221-224. |
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| 作者姓名： | 许绍元 |
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| 作者单位： | 赣南师范学院,数学与计算机科学学院,江西,赣州,341000 |
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| 基金项目： | 国家自然科学基金(10571185)，江西省自然科学基金(061105)资助项目 |
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| 摘 要： | 该文得到了自相似集存在最好Hs-几乎处处闭集覆盖的一个新充分必要条件,从而改进和推广了许绍元、李国祯在2004年的一个结果.作为应用,我们讨论了直线上的一个满足强分离开集条件的自相似集.
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| 关 键 词： | 自相似集 开集条件 Hausdorff测度与维数 最好Hs-几乎处处闭集覆盖 |
| 文章编号： | 1000-5862（2007）03-0221-04 |
| 修稿时间： | 2007-01-05 |
A New Sufficient and Necessary Condition Under Which Aself-Similar Set Has a Best -a.e.-Closed-Set Covering |
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| XU Shao-yuan.A New Sufficient and Necessary Condition Under Which Aself-Similar Set Has a Best -a.e.-Closed-Set Covering[J].Journal of Jiangxi Normal University (Natural Sciences Edition),2007,31(3):221-224. |
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| Authors: | XU Shao-yuan |
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| Institution: | School of Mathematics and Computer Science, Gannan Teachers College,Ganzhou Jiagxi 341000, China |
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| Abstract: | In this paper,a new sufficient and necessary condition for the existence of the best-a.e.-closed-set covering of the self-similar set is obtained.As a result,we improve and generalize a corresponding result which is obtained by Shaoyuan Xu and Guozhen Li in 2004.As applications,a self-similar set satisfying the strong separation open set condition,which is constructed on the real line is well discussed. |
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| Keywords: | self-similar s-set open set condition(OSC) Hausdorff measure and Hausdorff dimension best-a e -closed-set covering |
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