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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Measures invariant under a linear group
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by Larry Baggett PDF
Proc. Amer. Math. Soc. 94 (1985), 179-186 Request permission

Abstract:

This paper deals with the question of when there exists on a Euclidean space a nontrivial probability measure $\mu$ which is invariant under a group $\Gamma$ of integer matrices. Necessary conditions on $\Gamma$ and the dimension are discussed. It is shown that nontrivial examples do exist, but only in dimensions $\geqslant 6$. In fact, the only explicit example given is in dimension 10.
References
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 94 (1985), 179-186
  • MSC: Primary 28D15; Secondary 22D40
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0781078-4
  • MathSciNet review: 781078