= Strong c-monotonicity
{title2=$u(x)+v(y)\le c(x,y),\quad u+v=c\ \pi\text{-a.e.}$}
A <transport plan> is strongly c-monotone if Borel <Kantorovich potentials> satisfy the displayed feasible inequality everywhere and equality almost everywhere for the plan. Extended values $-\infty$ away from the full marginal-<measure> sets may be permitted. This is a potential certificate, not a strict version of every cyclic inequality. A finite continuous cost allows the <transport potential path construction>.
Back to article page
