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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 sets nonmeasurable with respect to invariant measures


Author: Sławomir Solecki
Journal: Proc. Amer. Math. Soc. 119 (1993), 115-124
MSC: Primary 43A05; Secondary 28A12, 28A20
MathSciNet review: 1159177
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Abstract: A group $ G$ acts on a set $ X$, and $ \mu $ is a $ G$-invariant measure on $ X$. Under certain assumptions on the action of $ G$ and on $ \mu $ (e.g., $ G$ acts freely and is uncountable, and $ \mu $ is $ \sigma $-finite), we prove that each set of positive $ \mu $-measure contains a subset nonmeasurable with respect to any invariant extensions of $ \mu $. We study the case of ergodic measures in greater detail.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1159177-1
PII: S 0002-9939(1993)1159177-1
Keywords: Invariant measures, nonmeasurable sets, extensions of measures
Article copyright: © Copyright 1993 American Mathematical Society