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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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Quasi-nilpotent sets in semigroups
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by H. L. Chow
Proc. Amer. Math. Soc. 52 (1975), 393-397
DOI: https://doi.org/10.1090/S0002-9939-1975-0374809-2

Abstract:

In a compact semigroup $S$ with zero $0$, a subset $A$ of $S$ is called quasi-nilpotent if the closed semigroup generated by $A$ contains $0$. A probability measure $\mu$ on $S$ is called nilpotent if the sequence $({\mu ^n})$ converges to the Dirac measure at $0$. It is shown that a probability measure is nilpotent if and only if its support is quasi-nilpotent. Consequently, the set of all nilpotent measures on $S$ is convex and everywhere dense in the set of all probability measures on $S$ and the union of their supports is $S$.
References
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 393-397
  • MSC: Primary 43A05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0374809-2
  • MathSciNet review: 0374809