Continuous ergodic measures on $R^{\infty }$ have disjoint powers
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- by Marek Kanter
- Proc. Amer. Math. Soc. 65 (1977), 332-337
- DOI: https://doi.org/10.1090/S0002-9939-1977-0443067-4
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Abstract:
If $\mu$ is an ergodic probability measure on an infinite dimensional linear measure space and if there exists an infinite sequence of measurable linear functional on this space such that all nontrivial linear combinations have continuous distribution under $\mu$, then the convolution powers of $\mu$ all live on disjoint sets.References
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Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 332-337
- MSC: Primary 60G30
- DOI: https://doi.org/10.1090/S0002-9939-1977-0443067-4
- MathSciNet review: 0443067