= Weak-star convergence in BV
{title2=$u_k\to u\text{ in }L^1,\quad Du_k\overset{*}{\rightharpoonup}Du$}
Convergence in the displayed sense combines strong function convergence with weak-star convergence of <derivative> <vector measures> against $C_0$ tests. Strong $L^1$ convergence and a uniform variation bound imply the <derivative> convergence by <integration by parts> and uniform test-function approximation. Conversely the <Uniform boundedness principle> bounds the <derivative> <measures> of a convergent sequence.
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