{"paper":{"title":"The core variety and representing measures in the truncated moment problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Grigoriy Blekherman, Lawrence Fialkow","submitted_at":"2018-04-12T01:56:21Z","abstract_excerpt":"The classical Truncated Moment problem asks for necessary and sufficient conditions so that a linear functional $L$ on $\\mathcal{P}_{d}$, the vector space of real $n$-variable polynomials of degree at most $d$, can be written as integration with respect to a positive Borel measure $\\mu$ on $\\mathbb{R}^n$. We work in a more general setting, where $L$ is a linear functional acting on a finite dimensional vector space $V$ of Borel-measurable functions defined on a $T_{1}$ topological space $S$. Using an iterative geometric construction, we associate to $L$ a subset of $S$ called the \\textit{core "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04276","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"}