变质量Wasserstein距离推广的障碍
Obstructions to extension of Wasserstein distances for variable masses
摘要：
我们研究的可能性，定义的距离在整个空间的措施，与属性，具有相同的质量的两个措施之间的距离是Wasserstein距离，到一个比例因子。我们证明了，在非常弱的自然条件下，如果底空间是无界的，那么标度因子一定是常数，与质量无关。此外，如果我们包括零测度，则不可能存在这样的距离。相反，我们提供的例子与非常数的比例因子的情况下，有界底空间。
英文摘要：
We study the possibility of defining a distance on the whole space of measures, with the property that the distance between two measures having the same mass is the Wasserstein distance, up to a scaling factor. We prove that, under very weak and natural conditions, if the base space is unbounded, then the scaling factor must be constant, independently of the mass. Moreover, no such distance can exist, if we include the zero measure. Instead, we provide examples with non-constant scaling factors for the case of bounded base spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
