Question

Difference between lebesgue measure and lebesgue outer measure

Answer 1

The open interval (a, b) has the same measure, since the difference between the two sets consists only of the end points a and b and has measure zero. Any Cartesian product of intervals [a, b] and [c, d] is Lebesgue-measurable, and itsLebesgue measure is (b − a)(d − c), the area of the corresponding rectangle.