A Daniell—Kolmogorov theorem for supremum preserving upper probabilities
Fuzzy Sets and Systems - Special issue on fuzzy measures and integrals
Fuzzy set-valued Gaussian processes and Brownian motions
Information Sciences: an International Journal
Approximations of upper and lower probabilities by measurable selections
Information Sciences: an International Journal
| Hi-index | 0.00 |
By the Choquet theorem, distributions of random closed sets can be characterized by a certain class of set functions called capacity functionals. In this paper a generalization to the multivariate case is presented, that is, it is proved that the joint distribution of finitely many random sets can be characterized by a multivariate set function being completely alternating in each component, or alternatively, by a capacity functional defined on complements of cylindrical sets. For the special case of finite spaces a multivariate version of the Moebius inversion formula is derived. Furthermore, we use this result to formulate an existence theorem for set-valued stochastic processes.