Approximate jump point ($u^{+},u^{-},{\nu }_u$)

A scalar function in the BV space has an approximate jump at a point when its mean on each of two half-balls approaches a different finite value. The half-balls are determined by a unit normal ${\nu }_u$. Reversing the normal exchanges the two BV traces on a hypersurface. Their collection is the jump set of a BV function.