## Electronic Communications in Probability

- Electron. Commun. Probab.
- Volume 7 (2002), paper no. 10, 97-100.

### Subdiagonal and Almost Uniform Distributions

#### Abstract

A distribution (function) $F$ on $[0,1]$ with $F(t)$ less or equal $t$ for all $t$ is called *subdiagonal*. The extreme subdiagonal distributions are identified as those whose distribution functions are almost surely the identity, or equivalently for which $F \circ F = F$. There exists a close connection to exchangeable random orders on $\{1,2,3,...\}$.

#### Article information

**Source**

Electron. Commun. Probab., Volume 7 (2002), paper no. 10, 97-100.

**Dates**

Accepted: 10 September 2001

First available in Project Euclid: 16 May 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.ecp/1463434777

**Digital Object Identifier**

doi:10.1214/ECP.v7-1051

**Mathematical Reviews number (MathSciNet)**

MR1902597

**Zentralblatt MATH identifier**

1010.60023

**Subjects**

Primary: 60E99: None of the above, but in this section

Secondary: 60E15: Inequalities; stochastic orderings 46A55: Convex sets in topological linear spaces; Choquet theory [See also 52A07]

**Keywords**

Subdiagonal distribution almost uniform distribution exchangeable random order

**Rights**

This work is licensed under aCreative Commons Attribution 3.0 License.

#### Citation

Ressel, Paul. Subdiagonal and Almost Uniform Distributions. Electron. Commun. Probab. 7 (2002), paper no. 10, 97--100. doi:10.1214/ECP.v7-1051. https://projecteuclid.org/euclid.ecp/1463434777