14 Case2:0∈Θ(e). Let Bn be the event that supoee()Q(@;Xn)-Qo()<6/2.Then, Bn→Q(0;Xn)>Qo(0)-δ/2 for all0 →Q(0o;Xn)>Qo(0o)-6/2 By comparing the last expressions for each of cases 1,2,we conclude that if both An and Bn hold then e(e).But by uniform convergence,pr(An Bn)→l,sopr(0∈Θ(e)→l.14 Case 2: θ ∈ Θ(). Let Bn be the event that supθ∈Θ() |Q(θ; Xn)−Q0(θ)| < δ/2. Then, Bn ⇒ Q(θ; Xn) > Q0(θ) − δ/2 for all θ ⇒ Q(θ0; Xn) > Q0(θ0) − δ/2 By comparing the last expressions for each of cases 1,2, we conclude that if both An and Bn hold then ˆ θ ∈ Θ(). But by uniform convergence, pr(An ∩ Bn) → 1, so pr( ˆ θ ∈ Θ()) → 1.