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Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on 𝕋
Published online by Cambridge University Press: 27 February 2009
Abstract
We prove that if a Borel probability measure on the circle group 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 the measure is either Lebesgue or has finite support.
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- Copyright © Cambridge University Press 2009
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