Loeb Extension and Loeb Equivalence

Abstract

Jerome Keisler and Yeneng Sun raised 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?

Publication
Minor revision requested (Proc. AMS)
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