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Also asked on math.SE. Let $(Z,d)$ be a metric space, and for $p\geq 1$, consider a metric space $(W_p,d_{W_p})$ defined by The Wasserstein Space $\begin{align}W_p = \{\mu|\mu\textrm{ is a Borel ...

Let $p \in [1, \infty)$. Let $\mathcal P_p(\mathbb R^d)$ be the space of all Borel probability measures on $\mathbb R^d$ with finite $p$-th moments. Let $D_p$ be the collection of all Borel measurable ...

Consider the product of two metric spaces $X\times Y$, and two probability distributions $\mu$ and $\nu$ on this product space. By the Kantorovich-Rubinstein duality, I can write the Wasserstein-1-...

This is a follow-up question to this question: Closure Wasserstein for pointmasses Let $(X,d)$ be a metric space, and let $W_1(X)$ be the space of probability measures $\mu$ on $X$ having finite first ...

I was looking at the closed form formula for 2-Wassersteins distance for multivariate normal distribution on Wikipedia. https://en.wikipedia.org/wiki/Wasserstein_metric#Normal_distributions It has a ...