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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The existence of nonmeasurable sets for invariant measures


Authors: Marcin Penconek and Piotr Zakrzewski
Journal: Proc. Amer. Math. Soc. 121 (1994), 579-584
MSC: Primary 04A15; Secondary 04A20, 28A05, 28C10
DOI: https://doi.org/10.1090/S0002-9939-1994-1182704-6
MathSciNet review: 1182704
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Abstract: We prove that if G is a locally compact Polish group acting in a reasonable way on a set X, then for every countably additive, $ \sigma $-finite, G-invariant measure on X there exist nonmeasurable sets. In particular, the latter is true when X is a compact, metric, metrically homogeneous space, and G is the group of its isometries.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1182704-6
Keywords: Action by a locally compact Polish group, invariant $ \sigma $-finite measure, nonmeasurable set
Article copyright: © Copyright 1994 American Mathematical Society