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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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DOI: https://doi.org/10.1090/S0002-9939-1988-0947672-5
Keywords: Hyperfinite factor, injective, invariant measure, category measure, ergodic action
Article copyright: © Copyright 1988 American Mathematical Society