A new proof, based on the duality theorem of linear programming, is given of a theorem of V. Strassen, which states essentially that the minimum distance between random variables with given distributions equals the Prokhorov distance of their distributions.
"Nearest Random Variables with Given Distributions." Ann. Probab. 2 (1) 163 - 166, February, 1974. https://doi.org/10.1214/aop/1176996763