a query on compact embedding for critical exponent

Question

Suppose $(u_n)$ is a bounded sequence in $W^{1,2}(\Omega)$ where $\Omega$ is abounded domain. Then by the reflexivity there exists a weakly convergent subsequence to it, that converges to, say, $u\in W^{1,2}(\Omega)$. By compact embedding $u_n\rightarrow u$ in $L^r(\Omega)$ for $1\leq r<2^*$. By this norm convergence we can say that there exists a subsequence such that $u_n(x)\rightarrow u(x)$ in $\Omega$. On employing the Egoroff's theorem we obtain $u_n\rightarrow u$ uniformly a.e. excpet on a set of measure arbitrarily small. now can it be said from this uniform convergence that $\int_{\Omega}u_n^{2^*}dx\rightarrow \int_{\Omega}u^{2^*}dx$?. Where am I going wrong?.