## The Annals of Mathematical Statistics

### Upper and Lower Probabilities Induced by a Multivalued Mapping

A. P. Dempster

#### 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 in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177698950

Digital Object Identifier
doi:10.1214/aoms/1177698950

Mathematical Reviews number (MathSciNet)
MR207001

Zentralblatt MATH identifier
0168.17501

JSTOR