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| 摘要: |
| 本文研究了度量空间中Hausdorff 测度与度量及纲函数的关系. 利用拓扑学及Hausdorff 测度论中一些性质, 构造了两反例来说明存在不等价纲函数g,h 和某一紧度量空间(ρ,X),使得Hρ,g与Hρ,h 对此紧度量空间等价等问题. 这些反例有助于从另一个角度理解文胜友、文志英[4]中主要结果. |
| 关键词: 度量 纲函数 Hausdorff测度 等价 |
| DOI： |
| 分类号:O174.12 |
| 基金项目:国家自然科学基金青年基金资助(11101148);中央高校基本科研业务费专项资金资助. |
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| TWO COUNTEREXAMPLES ABOUT HAUSDORFF MEASURE WITH RESPECT TO METRIC AND GAUGE FUNCTION |
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YAO Yuan-yuan
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| Abstract: |
| In this paper, we investigate the relationship among Hausdorff measure, metric and gauge function. By using some properties in topology and Hausdorff measure theory, we construct two counterexamples to illustrate problems such as whether there exist two inequivalent gauge functions g,h and a compact metric space (ρ,X) such that Hρ,g and Hρ,h are equivalent with respect to (ρ,X). These counterexamples can help us to understand the main results in Wen Shenyou and Wen Zhiying [4] better. |
| Key words: metric gange function Hansdorff measure equivalence |
