English

Loeb Extension and Loeb Equivalence

Logic 2022-10-11 v1 Probability

Abstract

In Keisler and Sun (2004), the authors raise several open problems on Loeb equivalences between various internal probability spaces. We provide counter-examples for the first two open problems. Moreover, we reduce the third open problem to the following question: Is the internal algebra generated by the union of two Loeb equivalent internal algebras a subset of the Loeb extension of any one of the internal algebra?

Cite

@article{arxiv.2010.01842,
  title  = {Loeb Extension and Loeb Equivalence},
  author = {Robert M. Anderson and Haosui Duanmu and David Schrittesser and William Weiss},
  journal= {arXiv preprint arXiv:2010.01842},
  year   = {2022}
}

Comments

10 pages

R2 v1 2026-06-23T19:02:03.125Z