Dependence of Hausdorff measure and dimension with the metric of the underlying space(Chinese)
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摘要: 讨论在Rn中具有嵌套结构的几何对象上构造新度量的问题. 主要结果是: K是Rn中 具有嵌套结构的几何对象, 那么对于任何一个的连续的纲函数h(t), 可以构造一个在K上的度量,在这个新的度量空间(K, p)中, 0Hh (K)+∞. 如果纲函数取h(t)=ts,那么 对于任意0K上的度量, 在 这个新的度量空间(K, p)中,Hh (K)=1并且有dimPK=dimBK=dimHK=s成立.
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关键词:
- 嵌套结构 /
- Hausdorff测度 /
- 度量
Abstract: This paper discussed the construction of metric space on the nested geometrical object. Given a nested geometrical object K in Rn and a continuous gauge function h(t), a new metric p was constructed on K such that 0Hh (K)+∞ in the new metric space (K, p). Particularly, if the gauge function is h(t)=ts, then for any positive finite number s, it's also possible to construct a new metric p on K such that ~$\mathscrHh (K)=1 anddimPK=dimBK=dimHK=s.-
Key words:
- nested geometrical objectHausdorff measuremetric /
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