{"paper":{"title":"Countable tightness in the spaces of regular probability measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Damian Sobota, Grzegorz Plebanek","submitted_at":"2014-05-11T12:09:00Z","abstract_excerpt":"We prove that if $K$ is a compact space and the space $P(K\\times K)$ of regular probability measures on $K\\times K$ has countable tightness in its $weak^*$ topology, then $L_1(\\mu)$ is separable for every $\\mu\\in P(K)$. It has been known that such a result is a consequence of Martin's axiom MA$(\\omega_1)$.\n  Our theorem has several consequences; in particular, it generalizes a theorem due to Bourgain and Todor\\v{c}evi\\'c on measures on Rosenthal compacta."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2527","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"}