On continuity of invariant measures
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- by Andrew Adler
- Proc. Amer. Math. Soc. 41 (1973), 487-491
- DOI: https://doi.org/10.1090/S0002-9939-1973-0328025-9
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Abstract:
Main Theorem. Let $\Phi$ be a set of transformations on a set $X$. The following conditions are then equivalent: (1) There is a noncontinuous finitely additive measure defined on all subsets of $X$ and invariant under all transformations in $\Phi$. (2) There is an integer $m$ such that for any finite subset $F$ of $\Phi$ there is a finite subset ${A_F}$ of $X$, with no more than $m$ elements, such that each $f$ in $F$ acts as a permutation on ${A_F}$.References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 487-491
- MSC: Primary 28A70; Secondary 43A07
- DOI: https://doi.org/10.1090/S0002-9939-1973-0328025-9
- MathSciNet review: 0328025