论文标题
有限加入，可计数和内部概率措施
Finitely-additive, countably-additive and internal probability measures
论文作者
论文摘要
我们讨论了通过内部概率度量来构建标准概率度量（称为降低措施的标准概率度量）的两种方法。我们表明，内部概率措施与其推下措施之间的沃斯坦（Wasserstein）距离是无限的。作为对标准概率理论的应用，我们表明，在可分离的度量空间上，每个有限添加的鲍勒概率度量$ p $都是且仅当空间完全界限时，仅在且仅当空间完全界定时就限制了一系列可计数的鲍尔概率指标。
We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an internal probability measure and its push-down measure is infinitesimal. As an application to standard probability theory, we show that every finitely-additive Borel probability measure $P$ on a separable metric space is a limit of a sequence of countably-additive Borel probability measures if and only if the space is totally bounded.
