# Measure of base distribution $G_0(A)$ in the Dirichlet process

I am studying the Dirichlet Process and I came across this rule that states that given a partition $$A_i's$$ over the space $$\Theta$$, which represents the space in which $$G_0$$ is drawn from, $$(G(A_1),G(A_2),...G(A_k)) \sim Dir(\alpha G_0(A_1),\alpha G_0(A_2),... \alpha G_0(A_k)$$

$$G(A_i)$$ indicates the measure of $$A_i$$, which is equal to the sum of the height of the "pickets", $$\pi_k$$ present in the space $$A_i$$. How do we determine the measure of $$G_0(A_i)$$ ? Is this the integral of the probability distribution of $$G_0$$ over the partition $$A_i$$ ? I am not sure.

I am not so familiar with measure theory, so I am just basing it on intuition.