Give an example, in terms of the risk set S, in which the conclusion of Theorem 1 is violated if S is not (a) closed from below, (b) bounded from below. Use a modification of Exercise 24 of Chapter 5...

Give an example, in terms of the risk set S, in which the conclusion of Theorem 1 is violated if S is not (a) closed from below,

(b) bounded from below.

Use a modification of Exercise 24 of Chapter 5 (namely, a different choice of P) to show that the conclusion of Theorem 1 can be true even when S is not closed from below.