Paradoxical decompositions and invariant measures
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- by Piotr Zakrzewski PDF
- Proc. Amer. Math. Soc. 111 (1991), 533-539 Request permission
Abstract:
Suppose $G$ is a certain group of bijections of a given set $X$. A subset $E$ of $X$ is countably $G$-paradoxical if it contains disjoint subsets $A,B$, each of which can be taken apart into countably many pieces that may be rearranged via $G$ to form a partition of $E$. We prove that the existence of a countably additive measure on $P(X)$ that normalizes $X$ and vanishes on all countably $G$-paradoxical sets implies the existence of a countably additive, $G$-invariant measure on $P(X)$ normalizing $X$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 533-539
- MSC: Primary 04A20; Secondary 03E05, 28A99
- DOI: https://doi.org/10.1090/S0002-9939-1991-1039268-4
- MathSciNet review: 1039268