Unions of Loeb nullsets

Author:
David A. Ross

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1883-1888

MSC (1991):
Primary 28E05; Secondary 03H05, 26E35

DOI:
https://doi.org/10.1090/S0002-9939-96-03274-1

MathSciNet review:
1317048

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**[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**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
28E05,
03H05,
26E35

Retrieve articles in all journals with MSC (1991): 28E05, 03H05, 26E35

Additional Information

**David A. Ross**

Affiliation:
Department of Mathematics, University of Hawaii at Manoa, Honolulu, Hawaii 96822

Email:
ross@math.hawaii.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03274-1

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

Article copyright:
© Copyright 1996
American Mathematical Society