IP-Dirichlet measures and IP-rigid dynamical systems: An approach via generalized Riesz products

摘要

If (n_k)k≥1 is a strictly increasing sequence of integers, a continuous probability measure σ on the unit circle T is said to be IP-Dirichlet with respect to (n_k)k≥1 if σ?(Σ_(k∈F) n_k) → 1 as F runs over all non-empty finite subsets F of N and the minimum of F tends to infinity. IP-Dirichlet measures and their connections with IP-rigid dynamical systems have recently been investigated by Aaronson, Hosseini and Lemańczyk. We simplify and generalize some of their results, using an approach involving generalized Riesz products.