Stopping time problem

Question

I have some difficulty understanding following problem. I need to show any non random time $T$ is a stopping time. I know that we have to show {$T\le t$} is $F_t$ measurable. When $t \le T$ this set becomes empty so it is in $F_t$. My problem is when $t > T$. How to show { $T \le t$ } is omega.I do not see it.

Thanks and any help is greatly appreciated.

Answer 1

Notice that $$\Omega\supset \{T\leqslant t\}\supset \{T\lt t\},$$ and the third set is $\Omega$ because its complement is empty.