Does the pointwise limit of a $W^{r,p}$- bounded sequence belong to $W^{r,p}$?

Question

Let $f_n,f:\mathbb R^d\to\mathbb R$ such that $$ f_n(x)\to f(x) \textrm{ for a.e. }x$$ as $n\to\infty$. Let $p\in(1,\infty)$, $r\in\mathbb N$. Suppose that there exists a constant $C\in[0,\infty)$ such that $$ \|f_n\|_{W^{r,p}} \leq C$$ for every $n\in\mathbb N\,$. Can I conclude that $f\in W^{r,p}$ ?