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Unions of Loeb nullsets
Author(s):
David
A.
Ross
Journal:
Proc. Amer. Math. Soc.
124
(1996),
1883-1888.
MSC (1991):
Primary 28E05;
Secondary 03H05, 26E35
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Abstract:
The union of every point-finite, completely measurable family of Loeb nullsets is itself a Loeb nullset, provided the nonstandard model satisfies a simple set-theoretic condition. One application of this result is that every Loeb measurable function into a metric space has a lifting.
References:
- [A]
- J. Aldaz, Compactness and Loeb measures (to appear).
- [C]
- N. Cutland (ed.), Nonstandard Analysis and its Applications, Cambridge University Press, Cambridge, England, 1988. MR 89m:03060
- [CK]
- C.C. Chang and H.J. Keisler, Model Theory, North Holland, Amsterdam, The Netherlands, 1973. MR 53:12927
- [F]
- D. H. Fremlin, Measurable functions and almost continuous functions, Manuscripta Math. 33 (1981), 387--405. MR 82e:28006
- [J]
- R. Jin, The isomorphism property versus the special model axiom, J. Symbolic Logic 57 (1992), 975--987. MR 94c:03079
- [K]
- E. M. Kleinberg, Infinitary combinatorics, Cambridge Summer School in Mathematical Logic, Lecture Notes in Math., Vol. 337, Springer, Berlin, 1973, pp. 361--418. MR 49:2400
- [KoP]
- G. Koumoullis and K. Prikry, The Ramsey property and measurable selections, J. Lond. Math. Soc. 28 (1983), 203--210. MR 85g:54010
- [KuP]
- J. Kupka and K. Prikry, The measurability of uncountable unions, Amer. Math. Monthly 91 (1984), 85--97. MR 85g:28015
- [R1]
- D. A. Ross, Compact measures have Loeb preimages, Proc. Amer. Math. Soc. 115 (1992), 365--370. MR 92i:28023
- [R2]
- ------, Lifting theorems in nonstandard measure theory, Proc. Amer. Math. Soc. 109 (1990), 809--822. MR 91b:03110
- [R3]
- ------, Measurable Transformations in Saturated Models of Analysis, Ph. D. Thesis, Univ. of Wisconsin--Madison, 1983.
- [R4]
- ------, The special model axiom in nonstandard analysis, J. Symbolic Logic 55 (1990), 1233-1242. MR 91h:03091
- [SB]
- K. D. Stroyan and J. M. Bayod, Foundations of Infinitesimal Stochastic Analysis, North Holland / Elsevier Science Publishers, Amsterdam, The Netherlands, 1986. MR 87m:60001
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Additional Information:
David
A.
Ross
Affiliation:
Department of Mathematics, University of Hawaii at Manoa, Honolulu, Hawaii 96822
Email:
ross@math.hawaii.edu
DOI:
10.1090/S0002-9939-96-03274-1
PII:
S 0002-9939(96)03274-1
Keywords:
Loeb measure,
nonstandard analysis,
compact measure,
Loeb nullset
Received by editor(s):
July 6, 1993
Received by editor(s) in revised form:
December 30, 1994
Communicated by:
Andreas Blass
Copyright of article:
Copyright
1996,
American Mathematical Society
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