2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156735Let $Ω$ 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 $\sim$.5 pagesFunctional Analysis28A12, 28B20text