The Annals of Mathematical Statistics

Upper and Lower Probabilities Induced by a Multivalued Mapping

A. P. Dempster

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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.

Article information

Source
Ann. Math. Statist. Volume 38, Number 2 (1967), 325-339.

Dates
First available: 27 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoms/1177698950

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoms/1177698950

Mathematical Reviews number (MathSciNet)
MR207001

Zentralblatt MATH identifier
0168.17501

Citation

Dempster, A. P. Upper and Lower Probabilities Induced by a Multivalued Mapping. The Annals of Mathematical Statistics 38 (1967), no. 2, 325--339. doi:10.1214/aoms/1177698950. http://projecteuclid.org/euclid.aoms/1177698950.


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