紧标号度量空间中的收敛性
Convergence in the space of compact labeled metric spaces
摘要：
一个标记的度量空间直观地说是一个度量空间连同一组特殊的点被理解为空间的几何边界。我们研究了最近引入的标记Gromov-Hausdorff距离的基本性质，该距离是经典Gromov-Hausdorff距离的扩展，它度量了两个标记度量空间的接近程度。我们提供了一个工具箱的结果特征收敛标记Gromov-Hausdorff距离。得到了标号度量空间的完备性结果和该空间子集的预紧性特征。将所得结果应用于标记度量空间中的旅行时反问题。
英文摘要：
A labeled metric space is intuitively speaking a metric space together with a special set of points to be understood as the geometric boundary of the space. We study basic properties of a recently introduced labeled Gromov-Hausdorff distance, an extension of the classical Gromov-Hausdorff distance, which measures how close two labeled metric spaces are. We provide a toolbox of results characterizing convergence in the labeled Gromov-Hausdorff distance. We obtain a completeness result for the space of labeled metric spaces and precompactness characterizations for subsets of the space. The results are applied to travel time inverse problems in a labeled metric space context.
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