=+20.4. The construction in Theorem 20.4 requires only Lebesgue measure on the unit interval. Use the theorem to prove the existence of Lebesgue measure on R.

First construct A, restricted to (-n, n] X . . . X (-n, n], and then pass to the limit (n -+ ). The idea is to argue from first principles, and not to use previous constructions, such as those in Theorems 12.5 and 18.2.