Using totally convex functionals and their Lagrangian liftings, the authors prove existence and uniqueness of Monge solutions for optimal transport between super-regular laws of random measures.
Entropic measure and Wasserstein dif- fusion
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Totally convex functions, $L^2$-Optimal transport for laws of random measures, and solution to the Monge problem
Using totally convex functionals and their Lagrangian liftings, the authors prove existence and uniqueness of Monge solutions for optimal transport between super-regular laws of random measures.