{"paper":{"title":"Remarks on mass transportation minimizing expectation of a minimum of affine functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander V. Kolesnikov, Nikolay Lysenko","submitted_at":"2015-12-09T15:18:30Z","abstract_excerpt":"We study the Monge--Kantorovich problem with one-dimensional marginals $\\mu$ and $\\nu$ and the cost function $c = \\min\\{l_1, \\ldots, l_n\\}$ that equals the minimum of a finite number $n$ of affine functions $l_i$ satisfying certain non-degeneracy assumptions. We prove that the problem is equivalent to a finite-dimensional extremal problem. More precisely, it is shown that the solution is concentrated on the union of $n$ products $I_i \\times J_i$, where $\\{I_i\\}$ and $\\{J_i\\}$ are partitions of the real line into unions of disjoint connected sets. The families of sets $\\{I_i\\}$ and $\\{J_i\\}$ ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02894","kind":"arxiv","version":2},"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"}