With S and T the stopping times for a sequence of -algebra , with for m<n.
How can I show that S+T is a stopping time?
You just have to use the definition of a stopping time...
Assuming S and T take their values in , S+T does too.
Now we have to check that , which is straightforward since
Since S is a stopping time, . And since is a sigma-algebra, a finite union of elements of will still be in .