## Definition 7.3.6: Measurable Sets and Lebesgue Measure

A set

*is (Lebesque) measurable if for every set***E***we have that***A**Ifm^{*}() = mA^{*}(A) + mE^{*}(comp(A))E

*is measurable, the non-negative number***E***m(*is the (Lebesgue) measure of the set*) = m***E**^{*}(*)***E***.***E**