Doubly stochastic measures with hairpin support
type: Item
instance of: scholarly article
title: Doubly stochastic measures with hairpin support
zbMATH Open document ID: 0629.60002
DOI: 10.1007/BF00353879
author: Howard Sherwood
author: Michael Taylor
publication date: 1988-01-01T00:00:00Z
review text: \textit{T. L. Seethoff} and \textit{R. C. Shiflett} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 41, 283-288 (1978; Zbl 0364.60019)] proved nice uniqueness theorems concerning doubly stochastic measures supported on the union of the graphs of two functions, but the existence theorems were more elusive. In this present paper, using a functional equations approach, not only uniqueness results but also existence theorems are obtained for doubly stochastic measures with support sets of the form \(g\cup g^{-1}\) where g is an increasing homeomorphism of [0,1] onto itself such that \(g(x)<x\) whenever \(0<x<1\).
Mathematics Subject Classification ID: 60A10
Mathematics Subject Classification ID: 28A35
Mathematics Subject Classification ID: 28A33
zbMATH DE Number: 4024375
zbMATH Keywords: uniqueness theorems
zbMATH Keywords: doubly stochastic measures
zbMATH Keywords: support sets
zbMATH Keywords: extreme doubly stochastic measure
MaRDI profile type: Publication
cites work: On extremal measures and subspace density
cites work: On the "indeterminate case" in the theory of a linear functional equation
cites work: A Remark on Extreme Doubly Stochastic Measures
cites work: Q3336431
cites work: Doubly stochastic measures with prescribed support
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4024375