UPPER AND LOWER PROBABILITIES INDUCED BY A MULTI-VALUED MAPPING.

A multivalued mapping from a space X to a space S carries a probability measure defined over subsets of X into a system of upper and lower probabilities over subsets of S. Some basic properties of such systems are explored. Other approaches to upper and lower probabilities are possible and some of these are related to the present approach. A distinctive feature of the present approach is a rule for conditioning, or more generally, a rule for combining sources of information. Finally, the context in statistical inference from which the present theory arose is sketched briefly.