Let $\Omega \subset \mathbb R^n$ be a Lyps open set. The Banach space $BV(\Omega)$ is defined as $$BV(\Omega)=\{u\in L^1(\Omega):\ |Du|(\Omega)<\infty\}\qquad \|u\|_{BV}=\|u\|_1+|Du|(\Omega)$$ where $|Du|(\Omega)$ is the total variation of the measure $Du$ over $\Omega$.
on this space are defined the weak* topology as $$u_n\overset{*}\to u\iff u_n\overset{L^1}\to u\ \land \ \forall \phi\in C^0_0(\Omega,\mathbb R^n)\ \int_\Omega Du_n\cdot \phi\ dx\to \int_\Omega Du\cdot \phi\ dx$$ and the intermediate topology as $$u_n\overset{int}\to u\iff u_n\overset{L^1}\to u\ \land \ |Du_n|(\Omega)\to |Du|(\Omega)$$ Is it true that, as the terminology suggest the intermediate convergence is stronger than the weak star one?
in both cases, are closed and bounded sets sequentially compact in the intermediate topology?