{"paper":{"title":"IP-Dirichlet measures and IP-rigid dynamical systems: an approach via generalized Riesz products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Sophie Grivaux","submitted_at":"2012-09-13T13:22:51Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2884","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}