Strict convergence in BV
= Strict convergence in BV
{title2=$u_k\to u\text{ in }L^1,\quad |Du_k|(\Omega)\to |Du|(\Omega)$}
Strict convergence combines <strong convergence> in $L^1$ with convergence of the <total variation seminorm>. It implies <weak-star convergence in BV> but does not make jump sets stable: <mollifications> of an interior step can converge strictly to the step while every approximant has an empty <jump set of a bounded-variation function>.