We describe a construction which associates to any median metric space a pseudometric satisfying the binary intersection property for closed balls. Under certain conditions, this implies that the resulting space is, in fact, an injective metric space, bilipschitz equivalent to the original metric. In the course of doing this, we derive a few other facts about median metrics, and the geometry of CAT(0) cube complexes. One motivation for the study of such metrics is that they arise as asymptotic cones of certain naturally occurring spaces.

中文翻译：

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中值和单射度量空间

我们描述了一种构造，它将满足封闭球的二元交叉属性的伪度量与任何中值度量空间相关联。在某些条件下，这意味着结果空间实际上是一个单射度量空间，bilipschitz 等价于原始度量。在这样做的过程中，我们得出了一些关于中值度量的其他事实，以及 CAT(0) 立方复合体的几何形状。研究此类度量的一个动机是它们作为某些自然发生空间的渐近锥出现。