{"paper":{"title":"Disintegration of positive isometric group representations on $\\mathrm{L}^p$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.RT","authors_text":"Jan Rozendaal, Marcel de Jeu","submitted_at":"2015-02-03T06:29:27Z","abstract_excerpt":"Let $G$ be a Polish locally compact group acting on a Polish space $X$ with a $G$-invariant probability measure $\\mu$. We factorize the integral with respect to $\\mu$ in terms of the integrals with respect to the ergodic measures on $X$, and show that $\\mathrm{L}^p(X,\\mu)$ ($1\\leq p<\\infty$) is $G$-equivariantly isometrically lattice isomorphic to an $\\mathrm{L}^p$-direct integral of the spaces $\\mathrm{L}^{p}(X,\\lambda)$, where $\\lambda$ ranges over the ergodic measures on $X$. This yields a disintegration of the canonical representation of $G$ as isometric lattice automorphisms of $\\mathrm{L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00755","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"}