hello

i know i can introduce a metric on sets with the symmetric difference:

$\displaystyle d(A,B):=(\mu A \triangle B)$ which is a Metric if we conside the equivalence relation $\displaystyle A \sim B$ for $\displaystyle d(A,B)=0$

But is this also correct for a finite outer measure $\displaystyle \mu^{\ast}$?