Weak convergence in $D^{1,p}(\mathbb{R}^n)$ and in $\mathcal{M}(\mathbb{R}^n)$

Question

What it means: $$u_n\rightharpoonup u ~\text{weakly in }~ D^{1,p}(\mathbb{R}^n)\\ |\nabla(u_n-u)|^p\rightharpoonup\mu ~\text{weakly in}~ \mathcal{M}(\mathbb{R}^n)\\|u_n-u|^{p^{*}}\rightharpoonup\nu ~\text{weakly in}~ \mathcal{M}(\mathbb{R}^n)$$

I have this definition :

I don't know how i must write the things correctly.

Thank you.