Theorem

Let $\lambda^{*}:\mathcal{P}(X)\to[0,\infty]$ is an outer measure, then: - $\mathcal{M}(\lambda^{*}):=\{ A\subset X:A \ \ \lambda^{*}$-measurable$\}$ is a σ-algebra. - $\lambda:\mathcal{M}(\lambda^{*})\to[0,\infty]$ is a measure.