  We consider the Monge-Kantorovich transport problem in an abstract measure
theoretic setting. Our main result states that duality holds if $c:X\times Y\to
[0,\infty)$ is an arbitrary Borel measurable cost function on the product of
Polish spaces $X,Y$. In the course of the proof we show how to relate a non -
optimal transport plan to the optimal transport costs via a ``subsidy''
function and how to identify the dual optimizer. We also provide some examples
showing the limitations of the duality relations.
