Integral representation of invariant functionals
type: Item
instance of: scholarly article
title: Integral representation of invariant functionals
zbMATH Open document ID: 0954.28010
author: Yanyan Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-05-08T00:00:00Z
review text: Let \(\Sigma\) be an algebra of subsets of a set \(S\) and \(B(S,\Sigma)\) the Banach space of all real-valued, totally \(\Sigma\)-measurable functions, i.e., the closure of the space of all real-valued \(\Sigma\)-simple functions with respect to the sup-norm \(\|\cdot\|_\infty\). The authors give a representation of all continuous functionals \(I: (B(S,\Sigma),\|\cdot\|_\infty)\to \mathbb{R}\) which are order invariant, i.e., which satisfy \(\Phi(I(f))= I(\Phi\circ f)\) for any order isomorphism \(\Phi:\mathbb{R}\to \mathbb{R}\) and \(f\in B(S,\Sigma)\).
reviewed by: Hans Weber
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 1441399
zbMATH Keywords: invariant functionals
zbMATH Keywords: space of measurable functions
zbMATH Keywords: Choquet integral
zbMATH Keywords: Sugeno integral
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6720
OpenAlex ID: W1981187679
cites work: Q4000151
cites work: Some quantities represented by the Choquet integral
cites work: Invariant functions on simple orders
cites work: Integral Representation Without Additivity
cites work: Subjective Probability and Expected Utility without Additivity
DOI: 10.1006/JMAA.2000.6720
description: scientific article; zbMATH DE number 1441399