Closed Separable Random Sets in Rd

Spaces <Omega, Sigma, P > of closed separable random subsets in Rd are studied. The theorem about the construction of the measure P of general type in such spaces is proved in the case when random sets are locally definite. The concept of strict separability of random sets under consideration is introduced. It is proved that the multi-point probability distribution functions of random closed strict separable sets have no any isolated discontinuity points.