{"paper":{"title":"The multidimensional truncated Moment Problem: The Moment Cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.OC"],"primary_cat":"math.FA","authors_text":"Konrad Schm\\\"udgen, Philipp J. di Dio","submitted_at":"2018-09-03T12:42:54Z","abstract_excerpt":"Let $\\mathsf{A}=\\{a_1,\\dots,a_m\\}$, $m\\in\\mathbb{N}$, be measurable functions on a measurable space $(\\mathcal{X},\\mathfrak{A})$. If $\\mu$ is a positive measure on $(\\mathcal{X},\\mathfrak{A})$ such that $\\int a_i d\\mu<\\infty$ for all $i$, then the sequence $(\\int a_1 d\\mu,\\dots,\\int a_m d\\mu)$ is called a moment sequence. By Richter's Theorem each moment sequence has a $k$-atomic representing measure with $k\\leq m$. The set $\\mathcal{S}_\\mathsf{A}$ of all moment sequences is the moment cone.\n  The aim of this paper is to analyze the various structures of the moment cone. The main results conce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00584","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"}