{"paper":{"title":"Lebesgue decomposition in action via semidefinite relaxations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jean-Bernard Lasserre (LAAS-MAC)","submitted_at":"2015-10-07T06:56:36Z","abstract_excerpt":"Given all (finite) moments of two measures $\\mu$ and $\\lambda$ on $\\R^n$, we provide a numerical scheme to obtain the Lebesgue decomposition $\\mu=\\nu+\\psi$ with $\\nu\\ll\\lambda$ and $\\psi\\perp\\lambda$. When$\\nu$ has a density in $L\\_\\infty(\\lambda)$ then we obtain two sequences of finite moments vectorsof increasing size (the number of moments) which converge to the moments of $\\nu$ and $\\psi$ respectively, as the number of moments increases. Importantly, {\\it no} \\`a priori knowledge on the supports of $\\mu, \\nu$ and $\\psi$ is required."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01842","kind":"arxiv","version":2},"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"}