This paper characterizes the maximum mean discrepancies (MMD) that metrize the weak convergence of probability measures for a wide class of kernels. More precisely, we prove that, on a locally compact, non-compact, Hausdorff space, the MMD of a bounded continuous Borel measurable kernel k, whose reproducing kernel Hilbert space (RKHS) functions vanish at infinity, metrizes the weak convergence of probability measures if and only if k is continuous and integrally strictly positive definite (i.s.p.d.) over all signed, finite, regular Borel measures. We also correct a prior result of Simon-Gabriel & Sch\"olkopf (JMLR, 2018, Thm.12) by showing that there exist both bounded continuous i.s.p.d. kernels that do not metrize weak convergence and bounded continuous non-i.s.p.d. kernels that do metrize it.

翻译：本文描述了最大平均值差异(MMD)的特点,这种差异使广泛一类内核的概率计量措施的趋同性弱。更确切地说,我们证明,在Hausdorf空间,一个封闭的连续连续波雷尔可测量内核的MMD,其再生产内核Hilbert空间(RKHS)的功能无穷无穷消失,其概率计量措施的趋同性弱,如果而且只有当 k是连续和完全确定(s.p.d.)的所有已签字的、有限的、常规的波雷尔措施(s.p.d.)时。我们还纠正了Simon-Gabriel & Sch\'olkopf(JMLR, 2018, Thm.12)的先前结果,表明存在两个不协调弱趋同的连续内核(s.p.d.d.c.nel),并约束连续的非.d.d.内核内核的内核。