Results on the intersection of randomly located sets

Abstract

Randomly generated subsets of a point-set A 0 in the k-dimensional Euclidean space Rk are investigated. Under suitable restrictions the probability is determined that a randomly located set which hits A 0. is a subset of A 0 . Some results on the expected value of the measure and the surface area of the common intersection-set formed by n randomly located objects and A 0 are generalized and derived for arbitrary dimension k.