Transport cost function
= Transport cost function
{title2=$c:X\times Y\to[0,\infty]$}
= Transport cost
{synonym}
The transport cost <function> assigns a cost to a unit of mass moved from $x$ to $y$. A <transport plan> has total cost $\int c\,d\pi$. Costs separating as $a(x)+b(y)$ have the same well-defined total for every coupling of fixed marginals.