  Given a compact space $K$ and a Banach space $E$ we study the structure of
positive measures on the product space $K\times B_{E^*}$ representing
functionals on $C(K,E)$, the space of $E$-valued continuous functions on $K$.
Using the technique of disintegration we provide an alternative approach to the
procedure of transference of measures introduced by Batty (1990). This enables
us to substantially strengthen some of his results, to discover a rich order
structure on these measures, to identify maximal and minimal elements and to
relate them to the classical Choquet order.
