mathematical objects-Wasserstein Distance Is a Metric is a result from the foundations of optimal transport. For mathematical objects be a Polish mathematical objects1 p < objectsp(X)mathematical objects objectsXmathematical objectsx0 Xmathematical objects, p(X)mathematical objects(,)mathematical objectsX Xmathematica. It helps organize the relationship between Monge maps, Kantorovich plans, duality, and Wasserstein geometry.