Change of Variables Formula for Pushforward Measures is a result from the foundations of optimal transport. For mathematical objects be a mathematical objects(Y, B)mathematical objectsT:X Ymathematical objects A/ Bmathematical objectsT\# objects(Y, B)mathematical objects(T\#)(B)=(T-1(B))mathematical objectsB Bmathema. It helps organize the relationship between Monge maps, Kantorovich plans, duality, and Wasserstein geometry.