# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

### Tom 215 / 2013

Studia Mathematica 215 (2013), 237-259 MSC: 37A25, 42A16, 42A55, 37A45. DOI: 10.4064/sm215-3-3

#### Streszczenie

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 recently been investigated by Aaronson, Hosseini and Lemańczyk. We simplify and generalize some of their results, using an approach involving generalized Riesz products.

#### Autorzy

• Sophie GrivauxCNRS, Laboratoire Paul Painlevé, UMR 8524
Université Lille 1
Cité Scientifique
59655 Villeneuve d'Ascq Cedex, France
e-mail

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