# outer measure and Sigma algebra of $\mu$-measurable sets

let $\mu_1$ and $\mu_2$ be two outer measures in space $X$. For all $E \subseteq X$ let $\mu(E)=max\{\mu_1(E),\mu_2(E)\}$ I have proved that $\mu$ is an outer measure, now I have to show that:

$M(\mu_1) \cap M(\mu_2) \subseteq M(\mu)$ , M(μ) is the sigma-algebra of μ-measurable sets.

Any help!

• indicator functions? – BCLC Dec 13 '15 at 19:11