Integral representation of linear functionals on spaces of unbounded functions

Authors:
Patrizia Berti and Pietro Rigo

Journal:
Proc. Amer. Math. Soc. **128** (2000), 3251-3258

MSC (2000):
Primary 28C05; Secondary 60A05

Published electronically:
April 28, 2000

MathSciNet review:
1694449

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

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Additional Information

**Patrizia Berti**

Affiliation:
Dipartimento di Matematica Pura ed Applicata “G. Vitali”, Università di Modena, via Campi 213/B, 41100 Modena, Italy

Email:
berti.patrizia@unimo.it

**Pietro Rigo**

Affiliation:
Dipartimento di Statistica “G. Parenti”, Università di Firenze, viale Morgagni 59, 50134 Firenze, Italy

Email:
rigo@ds.unifi.it

DOI:
https://doi.org/10.1090/S0002-9939-00-05510-6

Keywords:
Bounded charge,
expectation,
integral representation,
linear positive functional

Received by editor(s):
August 1, 1997

Received by editor(s) in revised form:
December 17, 1998

Published electronically:
April 28, 2000

Additional Notes:
This research was partially supported by M.U.R.S.T. 40% “Processi Stocastici”.

Communicated by:
David R. Larson

Article copyright:
© Copyright 2000
American Mathematical Society