{"paper":{"title":"Duality and quotient spaces of generalized Wasserstein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.MG","authors_text":"Nhan-Phu Chung, Thanh-Son Trinh","submitted_at":"2019-04-29T06:14:26Z","abstract_excerpt":"In this article, using ideas of Liero, Mielke and Savar\\'{e} in [21], we establish a Kantorovich duality for generalized Wasserstein distances $W_1^{a,b}$ on a generalized Polish metric space, introduced by Picolli and Rossi. As a consequence, we give another proof that $W_1^{a,b}$ coincide with flat metrics which is a main result of [25], and therefore we get a result of independent interest that $\\left(\\mathcal{M}(X), W^{a,b}_1\\right)$ is a geodesic space for every Polish metric space $X$. We also prove that $(\\mathcal{M}^G(X),W_p^{a,b})$ is isometric isomorphism to $(\\mathcal{M}(X/G),W_p^{a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12461","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"}