Prove (iii) of Theorem 12.4.2. Hint: If 0 satisfies the null hypothesis g(0) = 0, then testing

Prove (iii) of Theorem 12.4.2. Hint: If θ0 satisfies the null hypothesis g(θ0) = 0, then testing Ω0 behaves asymptotically like testing the null hypothesis D(θ0)(θ − θ0) = 0, which is a hypothesis of the form considered in part (ii) of the theorem.