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

Integral representation of linear functionals on spaces of unbounded functions / Berti, Patrizia; P., Rigo. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 128(2000), pp. 3251-3258.

Integral representation of linear functionals on spaces of unbounded functions

BERTI, Patrizia;
2000

Abstract

Let L be a vector lattice of real functions on a set Omega with 1 is an element of L, and let P be a linear positive functional on L. Conditions are given which imply the representation P(f) = integral fd pi, f is an element of L, for some bounded charge pi. As an application, for any bounded charge pi on a field F, the dual of L-1(pi) is shown to be isometrically isomorphic to a suitable space of bounded charges on F. In addition, it is proved that, under one more assumption on L, P is the integral with respect to a sigma-additive bounded charge.
128
3251
3258
Integral representation of linear functionals on spaces of unbounded functions / Berti, Patrizia; P., Rigo. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 128(2000), pp. 3251-3258.
Berti, Patrizia; P., Rigo
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/306100
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