Definition 7.3.6: Measurable Sets and Lebesgue Measure

A set E is (Lebesque) measurable if for every set A we have that

m^*(A) = m^*(A E) + m^*(A comp(E))

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

Context