论文标题
Gromov-Hausdorff-Prokhorov收敛序列中的球质量和半径
Mass and radius of balls in Gromov-Hausdorff-Prokhorov convergent sequences
论文作者
论文摘要
我们调查了Gromov-Hausdorff的一些属性 - Prokhorov收敛序列$（\ Mathsf {X} _N，D _ {\ MathSf {\ Mathsf {X} _N}，ν_{\ Mathsf {\ Mathsf {x} _n} _n} _n} _ probiption _ {我们正式认为，如果极限几乎肯定是非原子的，那么对于$ \ mathsf {x} _n $，带有小半径的$ n $ n $ open球必须具有很小的质量。相反，如果极限几乎肯定得到了完全支持，则每个封闭的球中的每个封闭的球，$ \ mathsf {x} _n $，质量很小的半径必须很小。我们没有要求任何新的结果，但是为我们找不到明确参考的属性提供了理由。
We survey some properties of Gromov--Hausdorff--Prokhorov convergent sequences $(\mathsf{X}_n, d_{\mathsf{X}_n}, ν_{\mathsf{X}_n})_{n \ge 1}$ of random compact metric spaces equipped with Borel probability measures. We formalize that if the limit is almost surely non-atomic, then for large $n$ each open ball in $\mathsf{X}_n$ with small radius must have small mass. Conversely, if the limit is almost surely fully supported, then each closed ball in $\mathsf{X}_n$ with small mass must have small radius. We do not claim any new results, but justifications are provided for properties for which we could not find explicit references.
