The object studied in this paper is a pair (ℝlsquo;,Y) where ℝlsquo; is a random surface in ℝ’N and Y a random vector field on ℝ’N. The pair is jointly stationary, i.e. its distribution is invariant under translations. The vector field Y is smooth outside ℝlsquo; but may have discontinuities on ℝlsquo;. Gauss’ divergence theorem is applied to derive a flow conservation law for Y. For ℝ1 this specializes to a well-known rate conservation law for point processes. As an application, relationships for the linear contact distribution of ℝlsquo; are derived.
