IP-Dirichlet measures and IP-rigid dynamical systems: an approach via   generalized Riesz products
  If $(n_{k})_{k\ge 1}$ is a strictly increasing sequence of integers, a continuous probability measure $\sigma $ on the unit circle $\mathbb{T}$ is said to be IP-Dirichlet with respect to $(n_{k})_{k\ge 1}$ if $\hat{\sigma}(\sum_{k\in F}n_{k})\to 1 $ as $F$ runs over all non-empty finite subsets $F$ of $\mathbb{N}$ and the minimum of $F$ tends to infinity. IP-Dirichlet measures and their connections with IP-rigid dynamical systems have been investigated recently by Aaronson, Hosseini and Lema\'nczyk. We simplify and generalize some of their results, using an approach involving generalized Riesz products. 
Sophie Grivaux
math.DS math.CA