BV trace on a hypersurface ($u^{+},u^{-}$)

A BV space function has two one-sided approximate mean BV traces on a hypersurface at almost every point of an oriented countably rectifiable hypersurface, with respect to Hausdorff measure. They agree outside its approximate discontinuity set. At an approximate jump point, they are the jump values, up to the choice of orientation.