{"paper":{"title":"Ordered Probability Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jimmie Lawson","submitted_at":"2016-12-09T23:06:56Z","abstract_excerpt":"Let $C$ be an open cone in a Banach space equipped with the Thompson metric with closure a normal cone. The main result gives sufficient conditions for Borel probability measures $\\mu,\\nu$ on $C$ with finite first moment for which $\\mu\\leq \\nu$ in the stochastic order induced by the cone to be order approximated by sequences $\\{\\mu_n\\},\\{\\nu_n\\}$ of uniform finitely supported measures in the sense that $\\mu_n\\leq \\nu_n$ for each $n$ and $\\mu_n\\to \\mu$, $\\nu_n\\to \\nu$ in the Wasserstein metric. This result is the crucial tool in developing a pathway for extending various inequalities on operato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03213","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"}