I am reading an article on Nevanlinna theory trough brownian motion and they say that $$g_r(0,z)\,\text dA(z) =\frac 12 \mathbb E[\text{time }Z_s\text{ spends in }\text dA(z)\text{ before exiting }D_r]$$ where $Z_s$ is a complex Brownian motion and $D_r = B_r(0)$ and $g_r(0,z) = \frac1{2\pi}\log \frac{r}{|z|}$ is the Green function satisfying that $g_r(a,b)$ is the potential at $a$ given a unit charge at $b$ inside the grounded shell $\partial D_r$.
I don't understand (maybe intuitively) the relation between such potential $g_r(z,0)$ and the time spent at $\text dA(z)$. Can anyone help me?