Definition (Convergence in Norm) For a sequence of functions \(\{f_n\}_{n\geq 1}\) of a normed space \((V, ||\cdot||)\) then we say that \(f_n\) converges with respect to norm \(||\cdot||\), written \(f_n\stackrel{||\cdot||}{\rightarrow}f\) (\(n\rightarrow\infty\)), if \[\lim_{n\rightarrow\infty}||f_n-f||=0.\]