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, -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 -finite measure,
nonmeasurable set

Article copyright:
© Copyright 1994
American Mathematical Society