Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-24T09:40:23.740Z Has data issue: false hasContentIssue false
  • English
  • Français

Maharam spectra of Loeb spaces

Published online by Cambridge University Press:  12 March 2014

Renling Jin  and
H. Jerome Keisler
Renling Jin
Affiliation:
Department of Mathematics, College of Charleston, Charleston, SC 29424, E-mail: jin@math.cocf.edu
H. Jerome Keisler
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, E-mail: keisler@math.wisc.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We characterize Maharam spectra of Loeb probability spaces and give some applications of the results.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 550 - 566
Copyright
Copyright © Association for Symbolic Logic 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Chang, C. C. and Keisler, H. J., Model theory, third ed., North-Holland, 1990.Google Scholar
[2]Fremlin, D., Measure algebras, The handbook of Boolean algebra (Monk, J.D. and Bonnet, R., editors), vol. 3, North-Holland, 1989, Chapter 22.Google Scholar
[3]Henson, C. W., The isomorphism property in nonstandard analysis and its use in the theory of Banach space, this Journal, vol. 39 (1974), pp. 717–731.Google Scholar
[4]Henson, C. W., Foundations of nonstandard analysis– A gentle introduction to nonstandard extension, Non-standard analysis: Theory and applications (Cutland, N.J., Henson, C. W., and Arkeryd, L., editors), Kluwer Academic Publishers, 1997.Google Scholar
[5]Jin, R., Distinguishing three saturation properties in nonstandard analysis, Annals of Pure and Applied Logic, accepted.Google Scholar
[6]Jin, R., The isomorphism property versus the special model axiom, this Journal, vol. 57 (1992), pp. 975–987.Google Scholar
[7]Jin, R., Better nonstandard universes with applications, Nonstandard analysis: Theory and applications (Cutland, N.J., Henson, C.W., and Arkeryd, L., editors), Kluwer Publishers, 1997.Google Scholar
[8]Jin, R. and Shelah, S., Compactness of Loeb spaces, this Journal, vol. 63 (1998), pp. 1371–1392.Google Scholar
[9]Jin, R., Possible size of an ultrapower of ω, Archive for Mathematical Logic, vol. 38 (1999), pp. 61–77.CrossRefGoogle Scholar
[10]Keisler, H. J., An infinitesimal approach to stochastic analysis, Memoirs of the American Mathematical Society, vol. 297 (1984).Google Scholar
[11]Keisler, H. J., Rich and saturated adapted spaces, Advances in Mathematics, vol. 128 (1997), pp. 242–288.CrossRefGoogle Scholar
[12]Keisler, H. J. and Schmerl, J. H., Making the hyperreal line both saturated and complete, this Journal, vol. 56 (1991), pp. 1016–1025.Google Scholar
[13]Koppelberg, S., Cardinalities of ultraproducts of finite sets, this Journal, vol. 45 (1980), pp. 574–584.Google Scholar
[14]Lindstrom, T., An invitation to nonstandard analysis, Nonstandard analysis and its application (Cutland, N., editor), Cambridge University Press, 1988.Google Scholar
[15]Miller, A. W., Set theoretic properties of Loeb measure, this Journal, vol. 55 (1990), pp. 1022–1036.Google Scholar
[16]Ross, D. A., Automorphisms of the Loeb algebra, Fundamenta Mathematicae, vol. 128 (1987), pp. 29–36.CrossRefGoogle Scholar
[17]Ross, D. A., The special model axiom in nonstandard analysis, this Journal, vol. 55 (1990), pp. 1233–1242.Google Scholar
[18]Ross, D. A., Compact measures have Loeb preimages, Proceedings of American Mathematical Society, vol. 115 (1992), pp. 365–370.CrossRefGoogle Scholar
[19]Ross, D. A., Loeb measure and probability, Nonstandard analysis: Theory and applications (Cutland, N.J., Henson, C. W., and Arkeryd, L., editors), Kluwer Publishers, 1997.Google Scholar