Axiomatic Method of Measure and Integration (III). Definition and Existence Theorem of the Lebesgue Measure (Yoshifumi Ito “Theory of Lebesgue Integral”, Chapter 5)

In this paper, we define the Lebesgue measure on Rd, (d ≥ 1) by prescribing the complete system of axioms. Then we prove the uniqueness and existence theorem of the Lebesgue measure. This is a new result.