Problem 3. (7 points) Let (R, C, λ) be the Lebesgue measure space and let f : R → R be a non-negative, measurable function. Define a sequence (fn)nEN of functions by . fn = ƒ · X[1,1] : R→ R, nЄN. (a) Show that the sequence (fn)nEN is increasing and converges pointwise to the function f X(0,1]: R→ R. (b) Show that last fdX = lim fdx. 818