Unbounded quasi-integrals

Rustad, Alf

doi:10.1090/S0002-9939-00-05541-6

Unbounded quasi-integrals
HTML articles powered by AMS MathViewer

by Alf Birger Rustad PDF

Proc. Amer. Math. Soc. 129 (2001), 165-172 Request permission

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

Johan F. Aarnes, Quasi-states and quasi-measures, Adv. Math. 86 (1991), no. 1, 41–67. MR 1097027, DOI 10.1016/0001-8708(91)90035-6
J. F. Aarnes: “Image transformations and attractors,” Dept. of Math., University of Trondheim, Preprint no. 2 (1994).
J. F. Aarnes: “Quasi-measures in locally compact spaces,” Norwegian University of Science and Technology, Preprint no. 1 (1996).
J. F. Aarnes and A. B. Rustad: “Probability and Quasi-measures -a new interpretation,” To appear in Math. Scand.
Walter Rudin, Real and complex analysis, 3rd ed., McGraw-Hill Book Co., New York, 1987. MR 924157
A. B. Rustad: “The multidimensional median as a quasi-measure,” Norwegian University of Science and Technology, Preprint no. 5 (1998).
G. Taraldsen: “Image-transformations and quasi-measures in locally compact Hausdorff spaces,” University of Trondheim, Preprint (1995).