  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.
