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

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

2008-04-22

arxiv.org/abs/0804.3586v2

Mathematics

Dynamical Systems

Scientific paper

We prove that if a Borel probability measure (\mu) 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 (\mu) is either
Lebesgue or has finite support.

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