$\mu^*$-measurable set

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Definition

Given an outer-measure, $\mu^*:H\rightarrow\bar{\mathbb{R} }_{\ge 0}$ (for a hereditary sigma-ring, $H$) we define a set, $A\in H$ as $\mu^*$-measurable if:

• $\forall B\in H\big[\mu^*(B)=\mu^*(B\cap A)+\mu^*(B-A)\big]$

See also

• The set of all $\mu^*$-measurable sets is a ring - an important step on the way to restricting an outer-measure to a measure

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TODO: More links, also link to page for the restriction of outer measure to measure directly, once such a page exists

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