Continuing Exercise 4 , let (left(f_{n} ight)) be a Cauchy sequence in (mathscr{G}_{0}) such that (left|f_{n}(boldsymbol{x}) ight| ightarrow 0) for all (boldsymbol{x}). Show that

Continuing Exercise 4 , let \(\left(f_{n}\right)\) be a Cauchy sequence in \(\mathscr{G}_{0}\) such that \(\left|f_{n}(\boldsymbol{x})\right| \rightarrow 0\) for all \(\boldsymbol{x}\). Show that \(\left\|f_{n}\right\|_{\mathscr{G}_{0}} \rightarrow 0\).