{"paper":{"title":"Weakly Consistent Extensions of Lower Previsions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Paolo Vicig, Renato Pelessoni","submitted_at":"2018-03-27T07:48:20Z","abstract_excerpt":"Several consistency notions are available for a lower prevision P assessed on a set D of gambles (bounded random variables), ranging from the well known coherence to convexity and to the recently introduced 2-coherence and 2-convexity. In all these instances, a procedure with remarkable features, called (coherent, convex, 2-coherent or 2-convex) natural extension, is available to extend P, preserving its consistency properties, to an arbitrary superset of gambles. We analyse the 2-coherent and 2-convex natural extensions, E_2 and E_2c respectively, showing that they may coincide with the other"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09940","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"}