X PROBLEMS and m Section 2.6 Nonmeasurable Sets 47 24. Show that if E1 and E2 are measurable, then m(E1 UE2)+m(E1 E2)=m(E1)+m(E2). X25. Show that the assumption that m(B₁) <00 is necessary in part (ii) of the theorem regarding continuity of measure. 26. Let (Ek be a countable disjoint collection of measurable sets. Prove that for any set A, n mA Ek - k=1 k=1 27. Let M' be any σ-algebra of subsets of R and m' a set function on M' which takes values in [0, 0], is countably additive, and such that m'(0) = 0. (i) Show that m' is finitely additive, monotone, countably monotone, and possesses the excision property. X (ii) Show that m' possesses the same continuity properties as Lebesgue measure. 28. Show that continuity of measure together with finite additivity of measure implies countable additivity of measure. 2.6 NONMEASURABLE SETS