I am studying measure theory and read this following sentence:
Suppose $\mu(E)<\infty$ and $f(x)$ is a measurable function on $E$. Then for any $0<p_0<\infty$, $\lim_{p\rightarrow p_0^-}\left\Vert f\right\Vert_p=\left\Vert f\right\Vert_{p_0}$
Does anyone knows why this is true?