Subdiagonal and almost uniform distributions
type: Item
instance of: scholarly article
title: Subdiagonal and almost uniform distributions
zbMATH Open document ID: 1010.60023
author: Paul Ressel
published in: Electronic Communications in Probability
publication date: 2003-02-25T00:00:00Z
full work available at URL: https://eudml.org/doc/122582
full work available at URL: paper10.abs.html
review text: The space \(W\) of almost uniform distributions contains those distributions whose functions \(F\) are almost surely (a.s.) the identity, i.e. for which \(F\circ F=F\). A distribution function \(F\) on \([0,1]\) is called subdiagonal if \(F([0,t])\leq t\) for all \(t\in [0,1]\). \textit{U. Hirth} and the author [J. Theor. Probab. 13, No. 3, 609-634 (2000; Zbl 0971.60016)] have shown a close connection between \(W\) and the extreme exchangeable random total orders on the natural number set \(N\). The present paper wants to point out another interesting property of the space \(W\), viz. that the compact and convex set \(K\) of all subdiagonal distributions on \([0,1]\) has as extreme points the almost uniform distributions of the space \(W\). A simple example shows that \(K\) is not a simplex.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 60E99
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 46A55
zbMATH DE Number: 1873761
zbMATH Keywords: subdiagonal distribution
zbMATH Keywords: almost uniform distribution
zbMATH Keywords: exchangeable random order
MaRDI profile type: Publication
OpenAlex ID: W2071103222
DOI: 10.1214/ECP.V7-1051
description: scientific article; zbMATH DE number 1873761