## The Annals of Mathematical Statistics

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

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

#### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1214/aoms/1177698950

**Mathematical Reviews number (MathSciNet)**

MR207001

**Zentralblatt MATH identifier**

0168.17501

**JSTOR**

links.jstor.org

#### Citation

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