=+13.9. Suppose that f ,, and f are finite-valued, F-measurable functions such that f.(w)-f(w) for w E A, where (A) < c (u a measure on ). Prove Egoroff's theorem: For each € there exists a subset B of A such that u(B) <€ and f.(w) - f(w) uniformly on A - B. Hint: Let B(%) be the set of w in A such that If(w) - f,(w) > k"' for some i z n. Show that B(*) | /Ø as n to, choose