{"paper":{"title":"Time functions and $K$-causality between measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.MP"],"primary_cat":"math-ph","authors_text":"Tomasz Miller","submitted_at":"2018-01-16T23:44:58Z","abstract_excerpt":"Employing the notion of a coupling between measures, drawn from the optimal transport theory, we study the extension of the Sorkin-Woolgar causal relation $K^+$ onto the space $\\mathscr{P}(\\mathcal{M})$ of Borel probability measures on a given spacetime $\\mathcal{M}$. We show that Minguzzi's characterization of $K^+$ in terms of time functions possesses a \"measure-theoretic\" generalization. Moreover, we prove that the relation $K^+$ extended onto $\\mathscr{P}(\\mathcal{M})$ retains its property of antisymmetry for $\\mathcal{M}$ stably causal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05505","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"}