Be $1\leq p \leq \infty$. If $(f_{n})_n$ is a cauchy sequence in $\mathcal{L}^p(E)$ that converge pointwise to $f$ almost everywhere , show that $f\in \mathcal{L}^p$ and $\displaystyle \lim_{n \to \infty}{ N_{p}(f_{n}-f)}=0$
thx
Be $1\leq p \leq \infty$. If $(f_{n})_n$ is a cauchy sequence in $\mathcal{L}^p(E)$ that converge pointwise to $f$ almost everywhere , show that $f\in \mathcal{L}^p$ and $\displaystyle \lim_{n \to \infty}{ N_{p}(f_{n}-f)}=0$
thx