Sow that if eiad0xt is a nonrandomized rule ie eiad0xt

Question

Suppose that the action space is (?, Bk ?), where ? ∈ Bk. Let X be a sample from P ∈ P, δ0(X) be a nonrandomized rule, and T be a sufficient statistic for P ∈ P. Show that if E[IA(δ₀(X))|T] is a nonrandomized rule, i.e., E[IA(δ₀(X))|T] = IA(h(T)) for any A ∈ Bk ?, where h is a Borel function, then δ₀(X) = h(T (X)) a.s. P.