Then by (12) there exists T > 0 such that t > T implies Therefore (13) implies that for each ( α, γ ) ∈ A × Γ there exist a neighborhood U ( α, γ ) ⊂ A × Γ and T ( α, γ ) ∈ R$_{+}$ such that The neighborhoods { U ( α, γ ) : α ∈ A, γ ∈ Γ } are a covering of the compact set A × Γ , and therefore there exists a finite subcovering thereof: { U$_{j}$ = U ( α$_{j}$, γ$_{j}$ ) } N j $_{=1}$. Let T$_{0}$ = max$_{j}$ T ( α$_{j}$ , γ$_{j}$ ) . We shall show that lim sup$_{n}$$_{→∞}$ ∥ ˆ β$_{n}$ ∥ ≤ T$_{0}$ a.s. Put for brevity Then and therefore (14) and the Law of Large Numbers imply while which shows that ultimately ∥ ˆ β$_{n}$ ∥ ≤ T$_{0}$ with probability one. 8 λ$_{n}$ ( ̂ α$_{n}$, ̂ β$_{n}$ ) = inf β ∈ B inf α ∈ $_{A}$λ$_{n}$ ( α, β ) ≤ λ$_{n}$ ( α$_{0}$, β$_{0}$ ) → λ$_{0}$ a . s . lim inf n →∞ inf ‖ β ‖ >T 0 inf α ∈ $_{A}$λ$_{n}$ ( α, β ) ≥ λ$_{0}$ + ξ 2 a . s ., inf ‖ β ‖ >T 0 inf α ∈ $_{A}$λ$_{n}$ ( α, β ) ≥ 1 n n ∑ i =1 inf α ∈ A,γ ∈ Γ inf t>T 0 ρ ( y$_{i}$ − tγ $^{′}$h ( x$_{i}$, α )) = min j =1 ,...,N 1 n n ∑ i =1 inf ( α,γ ) ∈ U$_{j}$ inf t>T 0 ρ ( y$_{i}$ − tγ $^{′}$h ( x$_{i}$, α )) , λ$_{n}$ ( α, β ) = 1 n n ∑ i =1 ρ ( y$_{i}$ − β $^{′}$h ( x$_{i}$, α )) . E inf t>T ρ ( y − tγ $^{′}$h ( x , α )) > 1 − δ − 2 ε. (13) E inf ( α 1 ,γ$_{1}$ ) ∈ U ( α,γ ) inf t>T ( α,γ $_{)}$ρ ( y − tγ ′ $_{1}$h ( x , α$_{1}$ )) > 1 − δ − 2 ε = λ$_{0}$ + ξ 2 . (14)