Weak and strong convergence on $W^{1,N}(\mathbb{R}^N)$

Question

Can someone help me to understand why if $$u_n(x)\rightarrow 0,\, \text{a.e in}\, \mathbb{R}^N$$

then $$u_n\rightharpoonup 0,\, \text{in}\, W^{1,N}(\mathbb{R}^N)$$

Thank you

Edit : $\|u_n\|_{1,N}$ is bounded