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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Unbounded quasi-integrals


Author: Alf Birger Rustad
Journal: Proc. Amer. Math. Soc. 129 (2001), 165-172
MSC (1991): Primary 28A25
Published electronically: June 14, 2000
MathSciNet review: 1694879
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Abstract | References | Similar Articles | Additional Information

Abstract:

Let $X$ be a locally compact Hausdorff space. We define a quasi-measure in $ X $, a quasi-integral on $C_0(X)$, and a quasi-integral on $C_c(X)$. We show that all quasi-integrals on $C_0(X)$ are bounded, continuity properties of the quasi-integral on $C_c(X)$, representation of quasi-integrals on $C_c(X)$in terms of quasi-measures, and unique extension of quasi-integrals on $ C_c(X)$ to $C_0(X)$.


References [Enhancements On Off] (What's this?)

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Additional Information

Alf Birger Rustad
Affiliation: Faculty of Mathematics, Norwegian University of Science and Technology, Sem Saelandsv 9, Gloshaugen, 7055 Dragvoll, Norway
Address at time of publication: Department of Mathematical Sciences, Lade Norwegian University of Science and Technology, 7491 Trondheim, Norway
Email: alfr@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05541-6
PII: S 0002-9939(00)05541-6
Received by editor(s): October 14, 1996
Received by editor(s) in revised form: March 22, 1999
Published electronically: June 14, 2000
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 2000 American Mathematical Society