The set of all mu*-measurable sets is a sigma-ring

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Currently in the notes stage, see Notes:The set of all mu*-measurable sets is a ring

Statement

Recall that given an outer-measure, $\mu^*:\mathcal{H}\rightarrow\bar{\mathbb{R} }_{\ge 0}$ (where $\mathcal{H}$ is a hereditary sigma-ring) that the set of all mu*-measurable sets is a ring. It is in fact not only a ring of sets but a $\sigma$-ring.