Let $\mathcal{F}$ be the Borel $\sigma$-algebra on $(0,\infty)$ and fix $t>0$. I'm trying to show that
$\sigma(\{[s,\infty):0
The intervals generating the $\sigma$-algebra on the left are contained in the set on the right. We may also check directly that the righthand set is a $\sigma$-algebra. So it suffices to show that
$\sigma(\{[s,\infty):0
How to proceed from here?
Thank you.