Skorohod's representation theorem for sets of probabilities

We characterize sets of probabilities, Pi, on a measure space (Omega, F), with the following representation property: for every measurable set of Borel probabilities, A, on a complete separable metric space, (M, d), there exists a measurable X : Omega -> M with A = {X(P) : P is an element of Pi}. If Pi has this representation property, then: if K-n -> K-0 is a sequence of compact sets of probabilities on M, there exists a sequence of measurable functions, X-n : Omega -> M such that X-n(Pi) = K-n and for all P is an element of Pi, P({omega: X-n(omega) -> X-0(omega)}) = 1; if the K-n are convex as well as compact, there exists a jointly measurable (K,omega) bar right arrow H(K,omega) such that H(K-n, Pi) equivalent to K-n and for all P is an element of Pi, P({omega : H(K-n, omega) -> H(K-0, omega)}) = 1.

skorohod's representation theorem; strongly zero one sets of probabilities; multiple prior models of choice

Skorohod's representation theorem for sets of probabilities Articles