{"paper":{"title":"Singularity versus exact overlaps for self-similar measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"K\\'aroly Simon, Lajos V\\'ag\\'o","submitted_at":"2017-02-22T13:12:11Z","abstract_excerpt":"In this note we present some one-parameter families of homogeneous self-similar measures on the line such that\n  - the similarity dimension is greater than $1$ for all parameters and\n  - the singularity of some of the self-similar measures from this family is not caused by exact overlaps between the cylinders.\n  We can obtain such a family as the angle-$\\alpha$ projections of the natural measure of the Sierpi\\'nski carpet. We present more general one-parameter families of self-similar measures $\\nu_\\alpha$, such that the set of parameters $\\alpha$ for which $\\nu_\\alpha$ is singular is a dense "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06785","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"}