{"paper":{"title":"Localisation for constrained transports I: theory","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Krzysztof J. Ciosmak","submitted_at":"2023-12-19T16:03:57Z","abstract_excerpt":"We investigate an analogue of the irreducible convex paving in the context of generalised convexity. Consider two Radon probability measures $\\mu,\\nu$ ordered with respect to a cone $\\mathcal{F}$ of functions on $\\Omega$ stable under maxima. Under the assumption that any $\\mathcal{F}$-transport between $\\mu$ and $\\nu$ is local, we establish the existence of the finest partitioning of $\\Omega$, depending only on $\\mu,\\nu$ and the cone $\\mathcal{F}$, into $\\mathcal{F}$-convex sets, called irreducible components, such that any $\\mathcal{F}$-transport between $\\mu$ and $\\nu$ must adhere to this pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.12281","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.12281/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}