Fubini's theorem for ultraproducts of noncommutative L_p-spaces

Let (M_i)_{i ∈ I}, (N_j) _{j ∈ J} be families of von Neumann algebras and U, U′ be ultrafilters in I, J, respectively. Let 1 ≤ p < ∞ and n ∈ ℕ. Let x₁,...,x_n in ∏ L_p (M _i) and y₁,...,y_n in ∏ L_p (N_j) be bounded families. We show the following equality (Equation presented) For p = 1 this Fubini type result is related to the local reflexivity of duals of C*-algebras. This fails for p = ∞.