{"paper":{"title":"On Sudakov's type decomposition of transference plans with norm costs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Sara Daneri, Stefano Bianchini","submitted_at":"2013-11-08T10:02:48Z","abstract_excerpt":"We consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost $|\\cdot|_{D^*}$ \\[ \\min \\bigg\\{\\int |\\mathtt T(x) - x|_{D^*} d\\mu(x), \\ \\mathtt T : \\mathbb R^d \\to \\mathbb R^d, \\ \\nu = \\mathtt T_\\# \\mu \\bigg\\}, \\] with $\\mu$, $\\nu$ probability measures in $\\mathbb R^d$ and $\\mu$ absolutely continuous w.r.t. $\\mathcal L^d$. The key idea in this approach is to decompose (via disintegration of measures) the Kantorovich optimal transportation problem into a family of transportation problems in $Z_\\mathfrak a\\times\\mathbb R^d$, where $\\{Z_\\mathfrak "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1918","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"}