{"paper":{"title":"Duality Theorems in Ergodic Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.PR"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Jairo K. Mengue","submitted_at":"2012-01-25T15:32:45Z","abstract_excerpt":"We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization.\n  Another class of problems is the following: suppose $\\sigma$ is the shift acting on Bernoulli space $X=\\{0,1\\}^\\mathbb{N}$, and, consider a fixed continuous cost function $c:X \\times X\\to \\mathbb{R}$. Denote by $\\Pi$ the set of all Borel probabilities $\\pi$ on $X\\times X$, such that, both its $x$ and $y$ marginal are $\\sigma$-invariant probabilities. We are interested "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5301","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"}