{"paper":{"title":"A moment problem for random discrete measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eugene Lytvynov, Tobias Kuna, Yuri Kondratiev","submitted_at":"2013-10-29T16:41:43Z","abstract_excerpt":"Let $X$ be a locally compact Polish space. A random measure on $X$ is a probability measure on the space of all (nonnegative) Radon measures on $X$. Denote by $\\mathbb K(X)$ the cone of all Radon measures $\\eta$ on $X$ which are of the form $\\eta=\\sum_{i}s_i\\delta_{x_i}$, where, for each $i$, $s_i>0$ and $\\delta_{x_i}$ is the Dirac measure at $x_i\\in X$. A random discrete measure on $X$ is a probability measure on $\\mathbb K(X)$. The main result of the paper states a necessary and sufficient condition (conditional upon a mild  a priori bound) when a random measure $\\mu$ is also a random discre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7872","kind":"arxiv","version":4},"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"}