Essential closedness of Mumford–Shah jump sets
= Essential closedness of Mumford–Shah jump sets
A <minimizer> of the <Mumford–Shah functional> with bounded <image signal> data has an essentially closed jump set: replacing $J_u$ by its relative closure adds no $(n-1)$-dimensional <measure>. Its complement supports a Sobolev representative. This regularity theorem connects a relaxed <SBV space> <minimizer> to the classical closed-edge formulation; it is not a property of every special bounded-variation function.