Daniell integral represented by Radon measures
type: Item
instance of: scholarly article
title: Daniell integral represented by Radon measures
zbMATH Open document ID: 0677.28007
DOI: 10.1007/BF02844847
publication date: 1989-01-01T00:00:00Z
review text: Let X be a Suslin space and L be a sublattice of C(X) such that for every \(x\in X\) there exists a function \(\phi\in L\) for which \(\phi\) (x)\(\neq 0\). It is shown that for any Daniell integral \(\mu\) : \(L\to {\mathbb{R}}\) there exists a Radon measure m on X such that \(L\subset {\mathcal L}^ 1(m)\) and \[ \mu (\phi)=\int \phi dm,\quad \forall \phi \in L. \] Moreover, the measure m may be uniquely determined by constraining it to be concentrated on a certain type of subset of X. The relation between \({\mathcal L}^ 1(m)\) and \({\mathcal L}^ 1(\mu)\) is examined in detail.
Mathematics Subject Classification ID: 28C05
Mathematics Subject Classification ID: 46G12
zbMATH DE Number: 4109069
zbMATH Keywords: representing measures
zbMATH Keywords: Suslin space
zbMATH Keywords: Daniell integral
zbMATH Keywords: Radon measure
author: Erik G. F. Thomas
author: Alessio Volcic
reviewed by: Rimas Norvaiša
MaRDI profile type: Publication
cites work: Q3317574
cites work: Q5571891
cites work: Determination and study of positive forms on spaces of functions. I
cites work: Q4052400
cites work: Notes on Integration
cites work: Un confronto tra l'integrale di Daniell-Stone e quello di Lebesgue
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 4109069