Jensen's inequality relative to matrix-valued measures
type: Item
instance of: scholarly article
title: Jensen's inequality relative to matrix-valued measures
zbMATH Open document ID: 1120.26010
author: Douglas Farenick
author: Fei Zhou
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-01-09T00:00:00Z
review text: Jensen's inequality states that if \((X,\Sigma,\mu)\) is a measure space with \(\mu(X)=1\), \(\alpha<\beta\), and \(f:X\to\mathbb R\) is an integrable function with \(f(X)\subset(\alpha,\beta)\), then \[ \mathcal I\Big(\int_X f\;d\mu\Big) \leq \int_X (\mathcal I\circ f) d\mu \] for every convex function \(\mathcal I: (\alpha,\beta)\to\mathbb R\). In this paper, Jensen's inequality is extended to both scalar-valued and matrix-valued probability measures.
reviewed by: Wing-Sum Cheung
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 60B05
zbMATH DE Number: 5083323
zbMATH Keywords: probability measure
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.05.008
OpenAlex ID: W2042109541
cites work: Q5749818
cites work: Q5465303
cites work: JENSEN'S OPERATOR INEQUALITY
cites work: Jensen's Trace Inequality in Several Variables
cites work: The Radon-Nikodym Theorem for the Bochner Integral
cites work: The decomposition of matrix-valued measures
DOI: 10.1016/J.JMAA.2006.05.008
description: scientific article; zbMATH DE number 5083323