A representation for volume involving interior reach
The interior reach at a boundary point of an \(n\)-dimensional convex body is the radius of the largest ball contained within the body which also includes the boundary point. The author shows: The volume of a convex body may be represented as an alternating sum of integrals of powers of the interior reach function. Each integral is over the boundary of the body and the integration is with respect to the appropriate Federer curvature measure.
scientific article; zbMATH DE number 537304