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Unbounded quasi-integrals

Author(s): Alf Birger Rustad
Journal: Proc. Amer. Math. Soc. 129 (2001), 165-172.
MSC (1991): Primary 28A25
Posted: June 14, 2000
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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 $C_0(X)$.

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J. F. Aarnes: ``Quasi-states and Quasi-measures,'' Advances in Mathematics, vol. 86 (1991). MR 92d:46152

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J. F. Aarnes: ``Image transformations and attractors,'' Dept. of Math., University of Trondheim, Preprint no. 2 (1994).

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J. F. Aarnes: ``Quasi-measures in locally compact spaces,'' Norwegian University of Science and Technology, Preprint no. 1 (1996).

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J. F. Aarnes and A. B. Rustad: ``Probability and Quasi-measures -a new interpretation,'' To appear in Math. Scand.

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W. Rudin: ``Real and complex analysis,'' 3d ed., McGraw-Hill Book Company, Singapore (1987). MR 88k:00002

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A. B. Rustad: ``The multidimensional median as a quasi-measure,'' Norwegian University of Science and Technology, Preprint no. 5 (1998).

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G. Taraldsen: ``Image-transformations and quasi-measures in locally compact Hausdorff spaces,'' University of Trondheim, Preprint (1995).

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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: 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
Posted: June 14, 2000
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 2000, American Mathematical Society

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