Riesz theorem for positive multilinear functions
type: Item
instance of: scholarly article
title: Riesz theorem for positive multilinear functions
zbMATH Open document ID: 1273.28011
DOI: 10.1134/S0001434612090283
published in: Mathematical Notes
publication date: 2013-01-09T00:00:00Z
review text: The Riesz theorem is a classical result of functional analysis, which states that an arbitrary real-valued continuous linear functional in the space of all continuous real functions on a compact Hausdorff space can be represented by an integral [\textit{F. Riesz}, C. R. 149, 974--977 (1910; JFM 40.0388.03)]. The author extends this result to continuous multilinear functionals on the Cartesian product of a finite number of spaces of all continuous real functions on compact Hausdorff spaces (Theorem 1).
Mathematics Subject Classification ID: 28C05
Mathematics Subject Classification ID: 46G25
zbMATH DE Number: 6123766
zbMATH Keywords: Riesz theorem
zbMATH Keywords: multilinear function
zbMATH Keywords: multilinear functional
zbMATH Keywords: real-valued Borel measure
author: V. I. Bakhtin
reviewed by: Mark Burgin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6123766