some bounded set Λ ∈ R d such that Indeed, | ∫ R $^{d}$∖ Λ ε$_{n}$ ( t ) φ − $^{1}$( t ) ψ ( t ) dt | ≤ Since by (13) ∫ R d ( (1 + t $^{2}$) − 1 ) − $^{m}$| φ − $^{1}$( t ) | dt is bounded, say, by some V$_{φ}$ and for ψ ∈ S as t → ∞ the value | ( (1 + t $^{2}$) 1 ) $^{m}$ψ ( t ) | converges to zero, the set Λ can be selected such that | ∫$_{R}$ $^{d}$∖ Λ ε$_{n}$ ( t ) φ − $^{1}$( t ) ψ ( t ) dt | < ξ. V ∫$_{R}$ $^{d}$∖ Λ ( 1 + t $^{2}$) − 1 ) − ( ¯ m + m ) | φ − $^{1}$( t ) || ( 1 + t $^{2}$) 1 ) $^{m}$ψ ( t ) | dt ≤ V sup R $^{d}$∖ Λ | ( 1 + t $^{2}$) 1 ) $^{m}$ψ ( t ) | ∫$_{R}$ d ( 1 + t $^{2}$) − 1 ) − $^{m}$| φ − $^{1}$( t ) | dt. sup R $^{d}$∖ Λ | ( 1 + t $^{2}$) − 1 ) $^{m}$ψ ( t ) | < ξV − 1 φ V − $^{1}$. Consider now the value of the functional ( ε$_{n}$φ − 1 − εφ − $^{1}$, ψ ) . Since the se- quence of continuous bounded functions ε$_{n}$ − ε converges to zero in S ∗ it converges to zero point-wise and uniformly on bounded Λ. Then for any ζ and Λ corresponding to ξ = 1 $_{2}$ζ we can find N such that Thus | γ$_{n}$ − γ | → 0 in S $^{∗}$. ■ for any n > N. It follows that ∣ ( φ − $^{1}$ε$_{n}$ − φ − $^{1}$ε, ψ )∣ ∣ < ζ. 36 sup Λ | ε$_{n}$ − ε$_{0}$ | ∣ ∫ φ − $^{1}$( t ) ψ ( t ) dt ∣ < ξ