EnglishLet 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.
| Data di pubblicazione: | 2000 |
| Titolo: | Integral representation of linear functionals on spaces of unbounded functions |
| Autore/i: | Berti, Patrizia; P., Rigo |
| Autore/i UNIMORE: | |
| Rivista: | |
| Volume: | 128 |
| Pagina iniziale: | 3251 |
| Pagina finale: | 3258 |
| Codice identificativo ISI: | WOS:000089180400014 |
| Codice identificativo Scopus: | 2-s2.0-23044523055 |
| Citazione: | 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. |
| Tipologia | Articolo su rivista |
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