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

• Autores: Manfred Einsiedler, Alexander Fish
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 30, Nº 1, 2010, págs. 151-157
• Idioma: inglés
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• Resumen

  • 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.