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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168255We 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.Dynamical Systems47A35, 22D40Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on $\T$text