Resumen de Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on T

Manfred Einsiedler, Alexander Fish

• 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.