Measures invariant under a linear group
Author: Larry Baggett
Journal: Proc. Amer. Math. Soc. 94 (1985), 179-186
MSC: Primary 28D15; Secondary 22D40
MathSciNet review: 781078
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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.
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