Let be a sequence of random variables and stopping times with respect to the sequence
As and for any , this implies that , and so is a stopping time.
Now, my question is, let assume that I am considering I know that in general, is not a stopping time. However, if I were to consider my birthday this year (a stopping time), which is a deterministic stopping time. At any time, I know exactly when my birthday occurs. Also, I know two days before my birthday i.e, . What kind of a formulated counterexample will show that is indeed a stopping time in this setting.