Transport potential path construction
= Transport potential path construction
Anchor a countable dense subset of a closed <c-cyclically monotone> support. Take the infimum of accumulated differences $c(x_{j+1},y_j)-c(x_j,y_j)$ along chains ending at a variable point. Cyclical monotonicity bounds this potential below on the support projection. Its cost transform gives the other potential, with equality on the support. Continuity makes both potentials <upper semicontinuous> and thus Borel.