| 贝西科维奇集的豪斯道夫测度为无穷大 |
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| 引用本文： | 马际华. 贝西科维奇集的豪斯道夫测度为无穷大[J]. 武汉大学学报(理学版), 2001, 47(1): 6-8 |
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| 作者姓名： | 马际华 |
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| 作者单位： | 武汉大学数学科学学院/非线性科学中心,湖北 武汉 430072 |
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| 基金项目： | 国家自然科学基金资助项目(202000133) |
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| 摘 要： | 给定一个概率向量P=(p
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| 关 键 词： | 贝西科维奇集 豪斯道夫测度 量纲 测度的微扰 |
| 文章编号： | 0253-9888(2001)01-0006-03 |
| 修稿时间： | 2000-10-12 |
The Besicovitch Sets HaveInfinite Hausdorff Measures |
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| MA Ji-hua. The Besicovitch Sets HaveInfinite Hausdorff Measures[J]. JOurnal of Wuhan University:Natural Science Edition, 2001, 47(1): 6-8 |
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| Authors: | MA Ji-hua |
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| Abstract: | For a fixed probability vector P=(p0,p1,…,pm-1)(m≥2),The Besicovitch set B is the set of points in the unit interval which contain j(0≤j≤m-1) in their m-adic expansions in the propotion pj((0≤j≤m-1)); it is known that B has Hausodrff dimension(-∑pjlogpj)/(logm),and its Hausdorff measures(under any gauge) are either zero or infinity.A kind of peturbation measures are employed to prove that the Besicovitch set has infinite Hausdorff measure in the dimension. |
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| Keywords: | Besicovitch sets Hausdorff measures gauges peturbation of measures |
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