Coarea formula for BV functions
= Coarea formula for BV functions
{title2=$|Du|(A)=\int_{\mathbb R}|D\chi_{\{u>t\}}|(A)\,dt$}
For a scalar function in the <BV space>, <derivative> variation is the integral of the relative perimeter <measures> of its <superlevel sets>. The formula holds on every Borel subset $A$ of the domain, not just for total mass. It converts the continuous <ROF denoising> problem into linked minimization problems for <finite-perimeter sets>.