Abstract
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 in Sects. 1 and 2. Other approaches to upper and lower probabilities are possible and some of these are related to the present approach in Sect. 3. A distinctive feature of the present approach is a rule for conditioning, or more generally, a rule for combining sources of information, as discussed in Sects. 4 and 5. Finally, the context in statistical inference from which the present theory arose is sketched briefly in Sect. 6.
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Dempster, A.P. (2008). Upper and Lower Probabilities Induced by a Multivalued Mapping. In: Yager, R.R., Liu, L. (eds) Classic Works of the Dempster-Shafer Theory of Belief Functions. Studies in Fuzziness and Soft Computing, vol 219. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44792-4_3
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DOI: https://doi.org/10.1007/978-3-540-44792-4_3
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