$\Pi _1^1$ sets of unbounded Loeb measure
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- Proc. Amer. Math. Soc. 124 (1996), 2205-2210 Request permission
Abstract:
For every $\Pi _{1}^{1}$ and non-Borel subset $P$ of an internal set $X$ in a $\aleph _{2}$ saturated nonstandard universe there exists an internal, unbounded, non-atomic measure $\mu$ so that $L(\mu )(P\triangle B)$ is not finite for any Borel set $B$ in $X.$References
- C. Ward Henson, Analytic sets, Baire sets and the standard part map, Canadian J. Math. 31 (1979), no. 3, 663–672. MR 536371, DOI 10.4153/CJM-1979-066-0
- Albert E. Hurd and Peter A. Loeb, An introduction to nonstandard real analysis, Pure and Applied Mathematics, vol. 118, Academic Press, Inc., Orlando, FL, 1985. MR 806135
- Renling Jin, Cuts in hyperfinite time lines, J. Symbolic Logic 57 (1992), no. 2, 522–527. MR 1169188, DOI 10.2307/2275286
- H. Jerome Keisler, Kenneth Kunen, Arnold Miller, and Steven Leth, Descriptive set theory over hyperfinite sets, J. Symbolic Logic 54 (1989), no. 4, 1167–1180. MR 1026596, DOI 10.2307/2274812
- H. Jerome Keisler and Steven C. Leth, Meager sets on the hyperfinite time line, J. Symbolic Logic 56 (1991), no. 1, 71–102. MR 1131731, DOI 10.2307/2274905
- Peter A. Loeb, Conversion from nonstandard to standard measure spaces and applications in probability theory, Trans. Amer. Math. Soc. 211 (1975), 113–122. MR 390154, DOI 10.1090/S0002-9947-1975-0390154-8
- Arnold W. Miller, Special subsets of the real line, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 201–233. MR 776624
- K. D. Stroyan and José Manuel Bayod, Foundations of infinitesimal stochastic analysis, Studies in Logic and the Foundations of Mathematics, vol. 119, North-Holland Publishing Co., Amsterdam, 1986. MR 849100
- Boško Živaljević, $U$-meager sets when the cofinality and the coinitiality of $U$ are uncountable, J. Symbolic Logic 56 (1991), no. 3, 906–914. MR 1129155, DOI 10.2307/2275060
- Boško Živaljević, Lusin-Sierpiński index for the internal sets, J. Symbolic Logic 57 (1992), no. 1, 172–178. MR 1150932, DOI 10.2307/2275183
Additional Information
- Bosko Zivaljevic
- Affiliation: Department of Computer Science, The University of Illinois at Urbana-Champaign, Urbana, Illinois 61801; E-mail address: zivaljev@cs.uiuc.edu
- Address at time of publication: Process Management Computer, International Paper, 3101 International Rd. E., Mobile, Alabama 36616
- Email: zivaljev@cs.uiuc.edu, BZIVALJE@ipaper.com
- Received by editor(s): July 5, 1994
- Received by editor(s) in revised form: January 31, 1995
- Communicated by: Andreas R. Blass
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2205-2210
- MSC (1991): Primary 03H04, 03E15, 28E05; Secondary 04A15
- DOI: https://doi.org/10.1090/S0002-9939-96-03318-7
- MathSciNet review: 1322942