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 ∫$_{Ω}$$_{⧹}$$_{Λ}$ V ( 1 + t $^{2}$) $^{m}$| ˆ ε$_{1}$$_{n}$ ( t ) − ε$_{1}$ ( t ) | ∣ ∣$^{˜}$ ψ ( t ) ∣ dt ∣ (˜ γ$_{n}$ − γ, ˜ ψ ) ∣ ≤ sup Λ ∣ ∣$^{˜}$ φ − 1 n ˆ ε$_{1}$$_{n}$ − φ − $^{1}$ε$_{1}$ ∣ ∫$_{Λ}$ ∣ ∣$^{˜}$ ψ ( t ) ∣ dt + ∫$_{Ω}$$_{\}$$_{Λ}$ V ( 1 + t $^{2}$) $^{m}$| ε$_{1}$ ( t ) | ∣ ∣$^{˜}$ ψ ( t ) ∣ dt + ∫$_{Ω}$$_{\}$$_{Λ}$ V ( 1 + t $^{2}$) $^{m}$| ˆ ε$_{1}$$_{n}$ ( t ) − ε$_{1}$ ( t ) | ∣ ∣$^{˜}$ ψ ( t ) ∣ dt, Pr(sup Λ ∣ ∣$^{ˆ}$ φ − 1 n ˆ ε$_{1}$$_{n}$ − φ − $^{1}$ε$_{1}$ ∣ > (∫$_{Λ}$ ∣ ∣$^{˜}$ ψ ( t ) ∣ dt ) − 1 ζ ) + Pr (∫$_{Ω}$$_{\}$$_{Λ}$ V ( 1 + t $^{2}$) $^{m}$| ε$_{1}$ ( t ) | ∣ ∣$^{˜}$ ψ ( t ) ∣ dt ) > ζ ) + Pr (∫$_{Ω}$$_{\}$$_{Λ}$ V ( 1 + t $^{2}$) $^{m}$| ˆ ε$_{1}$$_{n}$ ( t ) − ε$_{1}$ ( t ) | ∣ ∣$^{˜}$ ψ ( t ) ∣ dt ) > ζ ) it follows that Pr( ∣ (˜ γ$_{n}$ − γ, ˜ ψ ) ∣ > ζ ) ≤ 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 66