Continuity of the visibility function (Q1182625)

The visibility function \(v\) assigns to each point \(x\) of a fixed measurable set \(S\) in the Euclidean space \(E_ n\) the Lebesgue outer measure of \(st(x,S)\). The paper studies the behavior of the visibility function in the boundary of a Jordan domain \(S\). It is proved that the function \(v\) of a planar Jordan domain \(S\) is continuous precisely at the cone points of the boundary of \(S\), that a smooth point of \(bd S\) is a cone point and that the visibility function is continuous at smooth points.