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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On Sullivan's invariant measure problem

Authors: L. J. Bunce and J. D. Maitland Wright
Journal: Proc. Amer. Math. Soc. 103 (1988), 870-874
MSC: Primary 46L35; Secondary 28D15, 46L55
MathSciNet review: 947672
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Abstract: Sullivan has posed an invariant measure problem for which a positive answer is very plausible. It also seems highly plausible that hyperfinite AW*-factors are injective. Surprisingly, it turns out that one of these problems must have a negative solution. Specifically we show that either the hyperfinite Takenouchi-Dyer factor is not injective, or no $ G$-invariant category measure exists for any free, ergodic action of a countable nonamenable group $ G$ on a perfect Polish space.

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PII: S 0002-9939(1988)0947672-5
Keywords: Hyperfinite factor, injective, invariant measure, category measure, ergodic action
Article copyright: © Copyright 1988 American Mathematical Society