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arXiv · 0804.3586

Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on $\T$

Manfred Einsiedler·Alexander Fish
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Abstract

We prove that if a Borel probability measure (μ) on (\T) is invariant under the action of a "large" multiplicative semigroup (lower logarithmic density is positive) and the action of the whole semigroup is ergodic then (μ) is either Lebesgue or has finite support.

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Manfred Einsiedler, Alexander Fish. 2008-09-04. Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on $\T$. https://arxiv.org/abs/0804.3586

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