Brownian occupation time
= Brownian occupation time
{c}
The occupation time of a measurable set $A$ through time $t$ is $\int_0^t\mathbf1_{\{B_s\in A\}}ds$. The <occupation-times formula> expresses such integrals through <local time of a semimartingale>. Recurrence and the <Strong Markov property> imply that one-dimensional Brownian motion spends an unbounded total time in every nonempty open interval.