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Counterexamples in Nonstandard Measure Theory

Published online by Cambridge University Press:  20 November 2018

J. M. Aldaz  and
P. A. Loeb
J. M. Aldaz
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad Autόnoma de Madrid, 28049 Madrid, Spain, e-mail:[email protected]
P. A. Loeb
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, U.S.A. e-mail:[email protected]
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Abstract

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We show that several "good" properties of the standard part map on regular Hausdorff spaces do not hold for arbitrary Hausdorff spaces.

Keywords

28E0503H05Loeb measuresstandard part map
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 3 , 01 September 1995 , pp. 257 - 261
Copyright
Copyright © Canadian Mathematical Society 1995

References

[A1] A\àaz, J. M., A characterization of universal Loeb measurability for completely regular Hausdorffspaces, Canad. J. Math. (4) 44(1992), 673–690.Google Scholar
[A2] A\àaz, J. M., On compactness and Loeb measures, Proc. Amer. Math. Soc, to appear.Google Scholar
[An] Anderson, R. M., Star-finite representations of measure spaces, Trans. Amer. Math. Soc. 271(1982), 667— 687.Google Scholar
[H] Henson, C. W., Analytic sets, Baire sets and the standard part map, Canad. J. Math. 31(1979), 663–672.Google Scholar
[K] Kunen, K., Inaccessibility Properties of Cardinals, Ph.D. Thesis, Stanford University, 1968.Google Scholar
[L1] Loeb, P. A., Weak limits of measures and the standard part map, Proc. Amer. Math. Soc. 77(1979), 128— 135.Google Scholar
[L2] Loeb, P. A., Afunctional approach to nonstandard measure theory, Contemp. Math. 26(1984), 251—261.Google Scholar
[LR1] Landers, D. and Rogge, L., Universal Loeb-measurability of sets and of the standard part map with applications, Trans. Amer. Math. Soc. (1) 304(1987), 229–243.Google Scholar
[LR2] Landers, D. and Rogge, L., Nichtstandard Analysis, Springer-Verlag, 1994.Google Scholar
[Lux] Luxemburg, W. A. J., A general theory of monads. In: Applications of Model Theory to Algebra, Analysis and Probability, (ed. W. A. J. Luxemburg), Holt, Rinehart and Winston, 1969, 18-69.Google Scholar
[MH] Machover, M. and Hirschfleld, J., Lectures in Non-Standard Analysis, Lecture Notes in Math. 94, Springer- Verlag, 1968.Google Scholar
[RI] Render, H., Pushing down Loeb measures, Math. Scand. 72(1993), 61–84.Google Scholar
[R2] Render, H., Nonstandard topology on function spaces with applications to hyperspaces, Trans. Amer. Math. Soc. (1)336(1993), 101–119.Google Scholar
[Ro] Ross, D., Compact measures have Loeb preimages, Proc. Amer. Math. Soc. 115(1992), 365–370.Google Scholar
[S] Steen, L. A. and Seebach, J. A., Counterexamples in Topology, Springer-Verlag, 1986.Google Scholar