Counterexamples in Nonstandard Measure Theory
Canadian mathematical bulletin, Tome 38 (1995) no. 3, pp. 257-261

Voir la notice de l'article provenant de la source Cambridge University Press

We show that several "good" properties of the standard part map on regular Hausdorff spaces do not hold for arbitrary Hausdorff spaces.
DOI : 10.4153/CMB-1995-038-5
Mots-clés : 28E05, 03H05, Loeb measures, standard part map
Aldaz, J. M.; Loeb, P. A. Counterexamples in Nonstandard Measure Theory. Canadian mathematical bulletin, Tome 38 (1995) no. 3, pp. 257-261. doi: 10.4153/CMB-1995-038-5
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A\àaz, J. M., A characterization of universal Loeb measurability for completely regular Hausdorffspaces, Canad. J. Math. (4) 44(1992), 673–690. Google Scholar

A\àaz, J. M., On compactness and Loeb measures, Proc. Amer. Math. Soc, to appear. Google Scholar

Anderson, R. M., Star-finite representations of measure spaces, Trans. Amer. Math. Soc. 271(1982), 667— 687. Google Scholar

Henson, C. W., Analytic sets, Baire sets and the standard part map, Canad. J. Math. 31(1979), 663–672. Google Scholar

Kunen, K., Inaccessibility Properties of Cardinals, Ph.D. Thesis, Stanford University, 1968. Google Scholar

Loeb, P. A., Weak limits of measures and the standard part map, Proc. Amer. Math. Soc. 77(1979), 128— 135. Google Scholar

Loeb, P. A., Afunctional approach to nonstandard measure theory, Contemp. Math. 26(1984), 251—261. Google Scholar

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

Landers, D. and Rogge, L., Nichtstandard Analysis, Springer-Verlag, 1994. Google Scholar

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

Machover, M. and Hirschfleld, J., Lectures in Non-Standard Analysis, Lecture Notes in Math. 94, Springer- Verlag, 1968. Google Scholar

Render, H., Pushing down Loeb measures, Math. Scand. 72(1993), 61–84. Google Scholar

Render, H., Nonstandard topology on function spaces with applications to hyperspaces, Trans. Amer. Math. Soc. (1)336(1993), 101–119. Google Scholar

Ross, D., Compact measures have Loeb preimages, Proc. Amer. Math. Soc. 115(1992), 365–370. Google Scholar

Steen, L. A. and Seebach, J. A., Counterexamples in Topology, Springer-Verlag, 1986. Google Scholar

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