Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



${\Pi _{1}^{1}}$ sets of unbounded Loeb measure

Author: Bosko Zivaljevic
Journal: Proc. Amer. Math. Soc. 124 (1996), 2205-2210
MSC (1991): Primary 03H04, 03E15, 28E05; Secondary 04A15
MathSciNet review: 1322942
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [He] C. W. Henson, Analytic Sets, Baire Sets, and the Standard Part Map, Canadian J. Math. 31 (1979), 663-672. MR 80i:28019
  • [HuLo] A. E. Hurd and P. A. Loeb, An Introduction to Nonstandard Real Analysis, Academic Press, New York, 1985. MR 87d:03184
  • [Ji] R. Jin, Cuts in hyperfinite time lines, J. of Symbolic Logic 57 (1992), 522-527. MR 93j:03029
  • [KKLM] H.J. Keisler, K. Kunen, A. Miller and S. Leth, Descriptive Set Theory over Hyperfinite sets, J. Symbolic Logic 54 (4) (1989), 1167-1180. MR 91c:03040
  • [KeLe] H.J. Keisler and S. Leth, Meager Sets on the Hyperfinite Time Line, J. Symbolic Logic 56 (1) (1991), 71-102. MR 93a:03074
  • [Lo] P. A. Loeb, Conversion from Nonstandard to Standard Measure Space and Applications in Probability Theory, Trans.Amer.Math.Soc. 211 (1975), 113-122. MR 52:10980
  • [Mi] A. Miller, Special Subsets of the Real Line, Handbook of Set-Theoretical Topology (K. Kunene and J.E. Vaughan (), eds.), North Holland, Amsterdam, 1984, pp. 201-234. MR 86i:54037
  • [StBa] K. D. Stroyan and J. M. Bayod, Foundations of infinitesimal stochastic analysis, North-Holland, Amsterdam, 1986. MR 87m:60001
  • [Zi1] B. Zivaljevic, $U$-meager sets when the cofinality and the coinitiality of $U$ are uncountable, J. of Symbolic Logic 56 (1991), 906-914. MR 92k:03033
  • [Zi2] ------, Lusin-Sierpinski Index for the Internal Sets, J. of Symbolic Logic 57 (1992), 172-178. MR 94a:03096

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 03H04, 03E15, 28E05, 04A15

Retrieve articles in all journals with MSC (1991): 03H04, 03E15, 28E05, 04A15

Additional Information

Bosko Zivaljevic
Affiliation: Department of Computer Science, The University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 \indent{E-mail address}:
Address at time of publication: Process Management Computer, International Paper, 3101 International Rd. E., Mobile, Alabama 36616

Received by editor(s): July 5, 1994
Received by editor(s) in revised form: January 31, 1995
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1996 American Mathematical Society