BV translation estimate
= BV translation estimate
{c}
{title2=$\|w(\cdot-h)-w\|_1\le|h||Dw|(\mathbb R^n)$}
For a smooth function, integrate its directional <derivative> along each segment of length $|h|$ and then integrate in space. This gives the displayed bound with $\int|\nabla w|$. Smooth BV approximation and <sequential lower semicontinuity> give the same inequality for general functions in the <BV space>. Averaging it over a <mollifier> proves the <BV mollification error estimate>.