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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 

<img src='content_image/320998.jpg'>

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 

<img src='content_image/320995.jpg'>

and therefore (14) and the Law of Large Numbers imply 

while 

which shows that ultimately ∥ ˆ β$_{n}$ ∥ ≤ T$_{0}$ with probability one. 

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