Let $(X,d)$ be a Polish [metric space](/page/Metric%20Space), let $p \ge 1$, and let $\mu_k,\nu_k,\mu,\nu \in \mathcal P_p(X)$ for every $k \in \mathbb N$. Suppose that $\mu_k \to \mu$ and $\nu_k \to \nu$ narrowly. Suppose also that, for some point $x_0 \in X$,