{"paper":{"title":"On the lattice structure of the space of all Bochner integrable Banach lattice-valued functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Omid Zabeti","submitted_at":"2018-10-12T05:01:41Z","abstract_excerpt":"Suppose $(X,\\Sigma,\\mu)$ is a finite measure space, $E$ is a Banach lattice, and $B(X,E,\\mu)$ is the space of all Bochner integrable $E$-valued functions. In this note, we show that $B(X,E,\\mu)$ is a $KB$-space or has the sequential Fatou property if and only if so is $E$. Among this, some results about Bochner integral convergence in $B(X,E,\\mu)$, using order structure of $E$, have been proved, as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05356","kind":"arxiv","version":3},"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"}