Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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