On sets nonmeasurable with respect to invariant measures
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- by Sławomir Solecki PDF
- Proc. Amer. Math. Soc. 119 (1993), 115-124 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 115-124
- MSC: Primary 43A05; Secondary 28A12, 28A20
- DOI: https://doi.org/10.1090/S0002-9939-1993-1159177-1
- MathSciNet review: 1159177