Let $X$ be a Polish space, let $c:X\times X\to [0,\infty]$ be lower semicontinuous, and let $\mu,\nu\in \mathcal P(X)$. Then \begin{align*} \mathcal T_c(\mu,\nu) = \sup\left\{\int_X \varphi\,d\mu + \int_X \psi\,d\nu : \varphi(x)+\psi(y)\le c(x,y)\text{ for all }x,y\in X\right\}, \end{align*} where the supremum is taken over bounded continuous admissible pairs. Equivalently, the same value is obtained by allowing admissible pairs with $\varphi\in L^1(\mu)$ and $\psi\in L^1(\nu)$ whose positive and negative parts make the two displayed integrals well-defined. In particular, \begin{align*} \mathcal T_c(\mu,\nu) = \sup\left\{\int_X \varphi\,d\mu + \int_X \varphi^c\,d\nu : \varphi\in L^1(\mu),\ \varphi^c\text{ is }\nu\text{-measurable, and the integrals are well-defined}\right\}. \end{align*}