define meaurable set A is outer measurable iff A' is outer measurable.
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We will now define when a set is outer measure with respect to a particular outer measure. Definition: Let be a measurable space with outer measure . A subset of is said to be Outer Measurable or -Measurable if for all subsets of we have that $\mu^* (A) = \mu^*(A \cap E) + \mu^*(A \cap E^c)$.
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