{"paper":{"title":"Purely non-atomic weak L^p spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Denny H. Leung","submitted_at":"1996-07-12T00:00:00Z","abstract_excerpt":"Let $\\msp$ be a purely non-atomic measure space, and let $1 < p < \\infty$. If $\\weakLp\\msp$ is isomorphic, as a Banach space, to $\\weakLp\\mspp$ for some purely atomic measure space $\\mspp$, then there is a measurable partition $\\Omega = \\Omega_1\\cup\\Omega_2$ such that $(\\Omega_1,\\Sigma\\cap\\Omega_1,\\mu_{|\\Sigma\\cap\\Omega_1})$ is countably generated and $\\sigma$-finite, and that $\\mu(\\sigma) = 0$ or $\\infty$ for every measurable $\\sigma \\subseteq \\Omega_2$. In particular, $\\weakLp\\msp$ is isomorphic to $\\ell^{p,\\infty}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9607208","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"}