Definition:Stopping Time/Continuous Time

Definition
Let $\struct {\Omega, \Sigma, \sequence {\FF_t}_{t \ge 0}, \Pr}$ be a continuous-time filtered probability space.

Let $T : \Omega \to \closedint 0 \infty$ be a random variable.

We say that $T$ is a stopping time with respect to $\sequence {\FF_t}_{t \ge 0}$ :
 * $\set {\omega \in \Omega : \map T \omega \le t} \in \FF_t$

for each $t \in \hointr 0 \infty$.