The Continuity of the Visibility Function on a Starshaped Set
Gerald Beer · Canadian Journal of Mathematics · 1972
The visibility function assigns to each point x of a fixed measurable set E in a Euclidean space En the Lebesgue outer measure of S(x), the set {y : rx + (1 — r)y ∊ E for every r in [0, 1]}. The purpose of this paper is to determine sufficient conditions for the continuity of the function on the interor of a starshaped set.