  Let $\Omega$ denote an algebra of sets and $\mu$ a $\sigma$-finite measure.
We then prove that the completion of $\Omega$ under the pseudometric $d(A,B)$ =
$\mu^{\ast}(A \triangle B)$ is $\sigma$-algebra isomorphic and isometric to the
Caratheodory Extension of $\Omega$ under the equivalence relation $\sim$.
