## Inner and outer regular

"Let $\mu$ be a finite measure on the Borel sigma-algebra $\mathfrak{B}(X)$ of a metric space $X$.

Prove that the class $\mathfrak{B}$ of all Borel sets that are both inner and outer regular is a sigma algebra. Deduce that every Borel set is inner regular."

I have a hard time visualizing what the complement of the inner/outer regular set is and how it all fits together. Any help is appreciated. (I think this is #12 in chapter 2 or Pollard's prob text)

Thanks!
Rich