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April, 1967 Upper and Lower Probabilities Induced by a Multivalued Mapping
A. P. Dempster
Ann. Math. Statist. 38(2): 325-339 (April, 1967). DOI: 10.1214/aoms/1177698950


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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A. P. Dempster. "Upper and Lower Probabilities Induced by a Multivalued Mapping." Ann. Math. Statist. 38 (2) 325 - 339, April, 1967.


Published: April, 1967
First available in Project Euclid: 27 April 2007

zbMATH: 0168.17501
MathSciNet: MR207001
Digital Object Identifier: 10.1214/aoms/1177698950

Rights: Copyright © 1967 Institute of Mathematical Statistics

Vol.38 • No. 2 • April, 1967
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