We prove a version for random measures of the celebrated Kantorovich-Rubinstein duality theorem and we give an application to the coupling of random variables which extends and unifies known results.
Dedecker, J., Prieur, C., & De Fitte, P. R. (2006). Parametrized Kantorovich-Rubinštein theorem and application to the coupling of random variables (pp. 105–121). https://doi.org/10.1007/0-387-36062-x_5