Let $X$ and $Y$ be Polish spaces, let $\mu \in \mathcal{P}(X)$ and $\nu \in \mathcal{P}(Y)$, and let $c: X \times Y \to [0,\infty]$ be lower semicontinuous. Assume that the Kantorovich value
Assume moreover that whenever $\Gamma \subset X \times Y$ is a nonempty Borel $c$-cyclically monotone set and there exists a plan $\gamma \in \Pi(\mu,\nu)$ with $\gamma(\Gamma)=1$ and