Suppose we have a measure $\mu$ and a space $X$ such that $\mu(X)=1$, and a function $f \in L^r$ for some $r > 0$, where $L^r$ is defined in the usual way even for numbers less than $1$.
Show that $lim_{p \to 0} ||f||_p =$ exp$(\int $log$|f|d\mu)$, where we note that exp(-$\infty)=0$ by convention.
Stuck on this one. Trying to use Holder's! Thoughts?
