For a given separable C*-algebra $A$ and a state $\omega : A \rightarrow \mathbb{C}$ with the GNS-representation $\pi_\omega$, Effros established a connection between the barycentric decomposition of $\omega$ and the disintegration of $\pi_\omega$, using a special class of barycentric measures called orthogonal measures.

From the perspective of unital completely positive (UCP) maps, a state $\omega : A \rightarrow \mathbb{C}$ can be viewed as a UCP map with a one-dimensional, commutative range and $\pi_\omega$ be the corresponding minimal Stinespring dilation. In this talk, we take this approach for a UCP map $\phi : A \rightarrow B(H)$ with the minimal Stinespring dilation $V^* \rho V$, connecting the barycentric decomposition of $\phi$ and the disintegration of $\rho$ which 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. Further, we will see some applications of generalized orthogonal measures.

Finally, we will present our ongoing work on ergodic decomposition of equivariant UCP maps by considering an action of a group $G$ on a separable C*-algebra $A$.