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Upper and Lower Probabilities Induced by a Multivalued Mapping

A. P. Dempster
The Annals of Mathematical Statistics
Vol. 38, No. 2 (Apr., 1967), pp. 325-339
Stable URL: http://www.jstor.org/stable/2239146
Page Count: 15
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Upper and Lower Probabilities Induced by a Multivalued Mapping
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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 Sections 1 and 2. Other approaches to upper and lower probabilities are possible and some of these are related to the present approach in Section 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 Sections 4 and 5. Finally, the context in statistical inference from which the present theory arose is sketched briefly in Section 6.

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