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we make use of Theorem 15.4 in Billingsley (1968), i.e. we verify that for each positive ε and η , there exists a δ , 0 < δ < 1, and an integer n$_{0}$ such that 

Define 

where S$_{i}$ = M ∗ $_{n}$( τ + i $_{m}$δ ). 

For t$_{1}$ ≤ t ≤ t$_{2}$ we have 

The Cauchy-Schwarz inequality yields 

By the same argument as in the proof of (S1.2) it follows that 

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for any sequence γ$_{n}$ , n ∈ N , converging to 0. Taking the right-continuity of M ∗ n into 

