On set-valued measures

As a rule, a measure is a mapping from a IT-field of sets into the eet of reals, or more generally, into some Banach space. A concept of set-valued measure (SV -measure) is introdilced in the paper being a specific mapping from a 3~field of sets into a power set of a set. Properties of SV-measures are analyzed <l1nd illustrated on examples. Close relationship between SV-measures and a lJiieW nonstandard approach in artificial intelligence (AI) is explained. Then, the ~onstruction of factorization of the measures is mentioned, a special class of ITquasiatomic SV-measures is defined and corresponding characterization theorem i:~ proved. This class involves SV-measures ranging in a countable set which were ;:sed in modelling uncertainty in AI. It enables to answer one question arising in connection with this application.