{"paper":{"title":"Supports, regularity, and $\\boxplus$-infinite divisibility for measures of the form $(\\mu^{\\boxplus p})^{\\uplus q}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Hao-Wei Huang","submitted_at":"2012-09-25T22:37:13Z","abstract_excerpt":"Let $\\mathcal{M}$ be the set of Borel probability measures on $\\mathbb{R}$. We denote by $\\mu^{\\mathrm{ac}}$ the absolutely continuous part of $\\mu\\in\\mathcal{M}$. The purpose of this paper is to investigate the supports and regularity for measures of the form $(\\mu^{\\boxplus p})^{\\uplus q}$, $\\mu\\in\\mathcal{M}$, where $\\boxplus$ and $\\uplus$ are the operations of free additive and Boolean convolution on $\\mathcal{M}$, respectively, and $p\\geq1$, $q>0$. We show that for any $q$ the supports of $((\\mu^{\\boxplus p})^{\\uplus q})^{\\mathrm{ac}}$ and $(\\mu^{\\boxplus p})^{\\mathrm{ac}}$ contain the sa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5787","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"}