An isomorphism between the completion of an Algebra and its Caratheodory Extension

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dc.creatorTanaka, Jun
dc.date2008-03-12
dc.date.accessioned2026-07-07T09:26:23Z
dc.date.available2026-07-07T09:26:23Z
dc.descriptionLet $Ω$ denote an algebra of sets and $μ$ a $σ$-finite measure. We then prove that the completion of $Ω$ under the pseudometric $d(A,B)$ = $μ^{\ast}(A \triangle B)$ is $σ$-algebra isomorphic and isometric to the Caratheodory Extension of $Ω$ under the equivalence relation $\sim$.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/0803.1749
dc.identifierhttp://arxiv.org/abs/0803.1749
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156735
dc.subjectFunctional Analysis
dc.subject28A12, 28B20
dc.titleAn isomorphism between the completion of an Algebra and its Caratheodory Extension
dc.typetext

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