The following definition is from Karatzas/Shreve:
Consider the stopping time of the right-continuous filtration $\mathscr{F}_t$ given by $\sigma_D=\inf\{t >0 ;W_t \in D^c\}$ [$W_t$ is Brownian motion, $D$ is open and bounded]. We say that a point $a \in \partial D$ is regular for $D$ if $P^a(\sigma_D=0)=1$, i.e. a Brownian path started at $a$ does not immediately return to $D$.
I thought I understood this definition but obviously I am not: Let e.g. $D$ be the open unit ball. Why is now every boundary point of $D$ regular?! I mean if we start Brownian motion at the boundary, at $t=0$ it is clearly in $D^c$. It could then go either into $D$ or not. What is the (intuitive) reason that I will not go into $D$?