Consider the reduced crossed product $C(X)\rtimes_rG$. Let $\varphi$ be a positive linear functional on $C(X)\rtimes_rG$. Define the function $\phi: G \to C(X)^*$ by $\phi(g)(f)=\varphi(f\lambda_g),g \in G$ and $f \in C(X)$. Since $\varphi$ is a linear functional, $\phi$ is well-defined. Moreover, $\phi(g)$ is a positive linear functional on $C(X)$, this follows easily from the positivity of the linear functional $\varphi$. We denote this positive linear functional $\phi(g)$ by $\nu_g$.
Jun Tomiyama in his book "Invitation to $C^*$-algebras and Topological dynamics" says that $\varphi$ can be written as $\sum_g \oplus \nu_g$. I am confused as to what this notation stands for. Is this a direct sum? It seems like one.