{"paper":{"title":"More on measurable algebras and Rademacher systems with applications to analysis of Riesz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mikhail Popov","submitted_at":"2016-07-25T21:17:27Z","abstract_excerpt":"We find necessary and sufficient conditions on a family $\\mathcal{R} = (r_i)_{i \\in I}$ in a Boolean algebra $\\mathcal{B}$ under which there exists a unique positive probability measure $\\mu$ on $\\mathcal{B}$ such that $\\mu ( \\bigcap_{k=1}^n \\theta_k r_{i_k} ) = 2^{-n}$ for all finite collections of distinct indices $i_1, \\ldots, i_n \\in I$ and all collections of signs $\\theta_1, \\ldots, \\theta_n \\in \\{-1,1\\}$, where the product $\\theta x$ of a sign $\\theta$ by an element $x \\in \\mathcal{B}$ is defined by setting $1 x = x$ and $-1 x = - x = \\mathbf{1} \\setminus x$. Such a family we call a comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07482","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"}