Measures invariant under a linear group
Larry Baggett · Proceedings of the American Mathematical Society · 1985
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.