Loeb extension and Loeb equivalence
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- by Robert M. Anderson, Haosui Duanmu, David Schrittesser and William Weiss HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 8 (2021), 112-120
Abstract:
In [J. London Math. Soc. 69 (2004), pp. 258–272] Keisler and Sun leave open several questions regarding Loeb equivalence between internal probability spaces; specifically, whether under certain conditions, the Loeb measure construction applied to two such spaces gives rise to the same measure. We present answers to two of these questions, by giving two examples of probability spaces. Moreover, we reduce their third question to the following: Is the internal algebra generated by the union of two Loeb equivalent internal algebras a subset of their common Loeb extension? We also present a sufficient condition for a positive answer to this question.References
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Additional Information
- Robert M. Anderson
- Affiliation: Department of Economics, University of California, Berkeley, California 94720
- ORCID: 0000-0002-4674-1088
- Haosui Duanmu
- Affiliation: Department of Economics, University of California, Berkeley, California 94720
- MR Author ID: 1041235
- David Schrittesser
- Affiliation: Kurt Gödel Research Center, University of Vienna, Universitätsring 1, 1010 Vienna, Austria
- MR Author ID: 799455
- ORCID: 0000-0002-4622-2675
- William Weiss
- Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1, Canada
- MR Author ID: 181610
- Received by editor(s): July 29, 2020
- Received by editor(s) in revised form: December 7, 2020
- Published electronically: March 23, 2021
- Communicated by: Heike Mildenberger
- © Copyright 2021 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 8 (2021), 112-120
- MSC (2020): Primary 28E05; Secondary 03H05, 26E35
- DOI: https://doi.org/10.1090/bproc/78
- MathSciNet review: 4234059