{"paper":{"title":"The uniqueness of the Fisher metric as information metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"H\\^ong V\\^an L\\^e","submitted_at":"2013-06-06T16:33:11Z","abstract_excerpt":"We define a mixed topology on the fiber space $\\cup_\\mu \\oplus^n L^n(\\mu)$ over the space $\\mathcal{M}(\\Omega)$ of all finite non-negative measures $\\mu$ on a separable metric space $\\Omega$ provided with Borel $\\sigma$-algebra. We define a notion of strong continuity of a covariant $n$-tensor field on $\\mathcal{M}(\\Omega)$. Under the assumption of strong continuity of an information metric we prove the uniqueness of the Fisher metric as information metric on statistical models associated with $\\Omega$. Our proof realizes a suggestion due to Amari and Nagaoka to derive the uniqueness of the Fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1465","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"}