Integral representation of linear functionals on spaces of unbounded functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Integral representation of linear functionals on spaces of unbounded functions

Authors:	Patrizia Berti Pietro Rigo

Institution:	Dipartimento di Matematica Pura ed Applicata ``G. Vitali', Università di Modena, via Campi 213/B, 41100 Modena, Italy ; Dipartimento di Statistica ``G. Parenti', Università di Firenze, viale Morgagni 59, 50134 Firenze, Italy

Abstract:	Let be a vector lattice of real functions on a set $\Omega$ with $\boldsymbol{1}\in L$ , and let be a linear positive functional on . Conditions are given which imply the representation $P(f)=\int fd\pi$ , $f\in L$ , for some bounded charge $\pi$ . As an application, for any bounded charge $\pi$ on a field $\mathcal F$ , the dual of $L^1(\pi)$ is shown to be isometrically isomorphic to a suitable space of bounded charges on $\mathcal F$ . In addition, it is proved that, under one more assumption on , is the integral with respect to a $\sigma$ -additive bounded charge.

Keywords:	Bounded charge expectation integral representation linear positive functional

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