{"paper":{"title":"On Convergence of Conditional Expectation Operators","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"C. Bryan Dawson","submitted_at":"1994-12-05T17:46:25Z","abstract_excerpt":"Given an operator $T:U_X(\\Sigma)\\to Y$ or ${T:U(\\Sigma)\\to Y$, one may consider the net of conditional expectation operators $(T_\\pi)$ directed by refinement of the partitions $\\pi$. It has been shown previously that $(T_\\pi)$ does not always converge to $T$. This paper gives several conditions under which this convergence does occur, including complete characterizations when $X={\\bold R}$ or when $X\\sp *$ has the Radon-Nikod\\'ym property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9412211","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"}