ABSTRACT
By (7) in Theorem 4 (§2.7) every point in K is σ-measurable. So is every open set in K by Theorem 9 (§3.4). The comple ment D in K of a σ-measurable subset E of K is σ-measurable since 1 £>σ = σ — 1 ^ σ. If A and B axe σ-measurable then so is their union A U B since Ia v b & = (1 a&) V (1 #σ) for σ > 0, and the absolutely integrable differentials on K form a Ba nach lattice. (See the remarks following Theorem 3 (§2.4).) Finally the union E of a monotone sequence E\ C E^ C · · · of σ-measurable sets is σ-measurable since 1 e „ S 1 e which implies 1 En° /* 1E<7 with Ι^σ integrable by Theorem 3 (§2.7) on monotone convergence.
