Nuclear subspace of \(L^ 0\) and the kernel of a linear measure
type: Item
instance of: scholarly article
title: Nuclear subspace of \(L^ 0\) and the kernel of a linear measure
zbMATH Open document ID: 0626.60008
DOI: 10.1016/0047-259X(87)90075-3
author: Yoshiaki Okazaki
author: Yasuji Takahashi
published in: Journal of Multivariate Analysis
publication date: 1987-01-01T00:00:00Z
review text: Let E be a locally convex (separated) topological vector space (over \({\mathbb{R}}\), say) and \(L:E\to L^ 0(\Omega,{\mathcal F},P)\) be a continuous linear functional; L induces a cylindrical probability measure \(\mu\) on E'. The paper studies several questions relating L, L(E) and \(\mu\). One theorem is as follows: if E is an LF space then \(\mu\) is \(\sigma\)- additive iff \(x_ n\to 0\) in E implies that \(L(x_ n)\to 0\) P-a.s. Other theorems relate the nuclearity of E with the \(\sigma\)-additivity of \(\mu\) or the nuclearity of E' with a cylindrical measure \(\nu\) on E.
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 28C20
zbMATH DE Number: 4017987
zbMATH Keywords: cylindrical probability measure
zbMATH Keywords: nuclearity
reviewed by: Srishti D. Chatterji
MaRDI profile type: Publication
cites work: Q5583383
cites work: Q4169448
cites work: Random Linear Functionals
cites work: On the nuclearity of a dual space with the convergence in probability topology
cites work: On Almost Sure Convergence in Linear Spaces of Random Variables
cites work: Certain General Questions of the Theory of Probability Measures in Linear Spaces
cites work: Q4066086
cites work: Q5620935
full work available at URL: 0047-259x(87)90075-3
OpenAlex ID: W2012598406
description: scientific article; zbMATH DE number 4017987