  A classical result by Effros connects the barycentric decomposition of a
state on a C*-algebra to the disintegration of the GNS representation of the
state with respect to an orthogonal measure on the state space of the
C*-algebra. In this note, we take this approach to the space of unital
completely positive maps on a C*-algebra with values in B(H), connecting the
barycentric decomposition of the unital completely positive map and the
dis-integration of the minimal Stinespring dilation of the same. This
generalizes Effros' work in the non-commutative setting. We do this by
introducing a special class of barycentric measures which we call generalized
orthogonal measures. We end this note by mentioning some examples of
generalized orthogonal measures.
