Description:
Let (S, B, G ) and (T, C,Q) be probability spaces, with Q nonatomic, and H = {h in C : Q(H) > 0}. In some economic models, the following conditional law of large numbers (LLN) is requested. There are a probability space (O,A,P) and a process X = {Xt : t in T}, with state space (S, B), satisfying for each h in H, there is Ah in A with P(Ah) = 1 such that t --> X(t, w) is measurable and Q {t : X(t, w) in ·}