On weak stationarity and weak isotropy of processes of convex bodies and cylinders

Generalized local mean normal measures .z, z . Rd, are introduced for a nonstationary process X of convex particles. For processes with strictly convex particles it is then shown that X is weakly stationary and weakly isotropic if and only if .z is rotation invariant for all z . Rd. The paper is concluded by extending this result to processes of cylinders, generalizing Theorem 1 of Schneider (2003).