Stability of Wasserstein Distances and Optimal Plans under Moment Convergence is a result from the foundations of optimal transport. For mathematical objects be a Polish mathematical objectsp [1,)mathematical objectsx0 Xmathematical objects(N)N mathematical objects(N)N mathematical objectsp(X)mathematical objects, p(X)mathematical objectsN o. It helps organize the relationship between Monge maps, Kantorovich plans, duality, and Wasserstein geometry.