Exercise 1.3.12 If and are stopping times, then so are min(, ) and max(, ).

Exercise 1.3.12 If ν and θ are stopping times, then so are min(ν, θ) and max(ν, θ).

Let ν be any nonnegative integer random variable that is finite with probability one. Let Xn, n ≥ 0 be a random sequence. Then, Xν denotes the random variable that takes values Xν(ω)(ω).

The following result says that we cannot beat a fair game by using a stopping rule that is a bounded stopping time