Conic support measures

Abstract

The conic support measures localize the conic intrinsic volumes of closed convex cones in the same way as the support measures of convex bodies localize the intrinsic volumes of convex bodies. In this note, we extend the `Master Steiner formula' of McCoy and Tropp, which involves conic intrinsic volumes, to conic support measures. Then we prove H\"{o}lder continuity of the conic support measures with respect to the angular Hausdorff metric on convex cones and a metric on conic support measures which metrizes the weak convergence.