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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A05, 28A12, 28A20

Retrieve articles in all journals with MSC: 43A05, 28A12, 28A20

Additional Information

Keywords: Invariant measures, nonmeasurable sets, extensions of measures
Article copyright: © Copyright 1993 American Mathematical Society