The question is the following
This question considers the occupation time of Brownian motion on the positive half time $\int_0^1 \mathbb{1}_{\{B_t >0\}}dt$.
Show that the functional $\psi$ on $C[0,1]$ defined by $$\psi(f)=\int_0^1 \mathbb{1}_{\{f(t) >0\}}dt$$ is continuous except on a set of Wiener measure 0.
I have no idea how to translate this to an actual argument. How exactly does a set of Wiener measure 0 look like?