Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am trying to verify that the object they define as $\mathcal F_\tau$ is indeed a sigma algebra. I am having trouble proving it's closed under complements relative to $\Omega$. I know the meaning of all the terms involved, so those do not need to be explained. (Like sigma algebra, stopping time, etc.) Thanks.

Oops. As pointed out I forgot to include a critical link

share|cite|improve this question
What do you mean by $\mathcal F_t$, is $t$ a stopping time? – Mohamad Mar 1 '13 at 2:09
up vote 2 down vote accepted

Note that there's a typo in Wikipedia's definition of $\mathcal{F}_\tau$. It defines $$\mathcal{F}_\tau = \{ A \in \mathcal{F} : \tau \cap A \in \mathcal{F}_t, t \ge 0 \}$$ but $\tau \cap A$ doesn't make sense. The correct definition should be $$\mathcal{F}_\tau = \{ A \in \mathcal{F} : \{\tau \le t\} \cap A \in \mathcal{F}_t, t \ge 0 \}.$$

For showing that $\mathcal{F}_\tau$ is closed under complements, here's a hint: for any sets $A,B$, we have $A^c \cap B = (A \cap B)^c \cap B$. (Draw a Venn diagram if you like.)

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.