{"paper":{"title":"Commutativity of integral quasi-arithmetic means on measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dorota G{\\l}azowska, Janusz Matkowski, Paolo Leonetti, Salvatore Tringali","submitted_at":"2017-03-11T10:01:24Z","abstract_excerpt":"Let $(X, \\mathscr{L}, \\lambda)$ and $(Y, \\mathscr{M}, \\mu)$ be finite measure spaces for which there exist $A \\in \\mathscr{L}$ and $B \\in \\mathscr{M}$ with $0 < \\lambda(A) < \\lambda(X)$ and $0 < \\mu(B) < \\mu(Y)$, and let $I\\subseteq \\mathbf{R}$ be a non-empty interval. We prove that, if $f$ and $g$ are continuous bijections $I \\to \\mathbf{R}^+$, then the equation $$ f^{-1}\\!\\left(\\int_X f\\!\\left(g^{-1}\\!\\left(\\int_Y g \\circ h\\;d\\mu\\right)\\right)d \\lambda\\right)\\! = g^{-1}\\!\\left(\\int_Y g\\!\\left(f^{-1}\\!\\left(\\int_X f \\circ h\\;d\\lambda\\right)\\right)d \\mu\\right)$$ is satisfied by every $\\mathscr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03938","kind":"arxiv","version":2},"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"}