content_image/301532.jpg content_image/301533.jpg content_image/301534.jpg
set Λ defined by Lemma 3 and show that Pr( ∣ (˜ γ$_{n}$ − γ, ˜ ψ ) ∣ > ζ ) goes to zero. ∗ 

Since ˆ ε$_{1}$$_{n}$ − ε$_{1}$ converges to zero in probability in S by Lemma 3 and since on Ω this difference is a continuous function, then also | ˆ ε$_{1}$$_{n}$ ( t ) − ε$_{1}$ ( t ) | converges to zero in probability in S ∗ on Ω. Thus 

converges in probability to zero. Then since 

it follows that Pr( ∣ (˜ γ$_{n}$ − γ, ˜ ψ ) ∣ > ζ ) ≤ 

<img src='content_image/301532.jpg'>

<img src='content_image/301533.jpg'>

<img src='content_image/301534.jpg'>

Here as shown in the Step 2 the first probability converges to zero, the second converges to zero by assumption 6 on ε$_{1}$, definition of the set Λ 

