On some metrics compatible with the Fell-Matheron topology
On some metrics compatible with the Fell-Matheron topology
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DOI：
10.1016/j.ijar.2006.12.008
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发表时间：
2007-09
期刊：
影响因子：
--
通讯作者：
Y. Ogura
中科院分区：
文献类型：
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作者：
Y. Ogura
修改 Hausdorff-Buseman 度量，我们在局部紧 Hausdorff 第二可数空间的闭子集空间上获得了与 Fell-Matheron 拓扑兼容的度量。我们还给出了该度量的替代表达式，以及两个更兼容的度量，求和形式的度量和修改的 Rockafellar-Wets 度量。通过研究原Hausdorff-Buseman度量与Rockafellar-Wets度量之间的关系，还表明在RN非空闭子集空间中原Hausdorff-Buseman度量的收敛性等价于Painlevé-Kuratowski收敛性。
Modifying the Hausdorff–Buseman metric, we obtain a compatible metric with the Fell–Matheron topology on the space of closed subsets of a locally compact Hausdorff second countable space. We also give an alternative expression of this metric, and two more compatible metrics, a metric of summation form and a modified Rockafellar–Wets metric. Through the study of the relation between the original Hausdorff–Buseman metric and the Rockafellar–Wets metric, it is also shown that the convergence in the original Hausdorff–Buseman metric in the space of non-empty closed subsets of RNis equivalent to the Painlevé–Kuratowski convergence.