. if x = y 2. Let (X, A, u) = (Y,B, v) = (N, M,c). Here, N is the set of natural numbers, M= 2N, and c is the counting measure defined by setting c(E) equal to the number of points in E if E is finite and oo if E is an infinite set. Define f: NN R by setting 2 - 2-3 f(x, y) -2 + 2-3 if x = y +1 0 otherwise. Show that (i) f is measurable with respect to the product measure c X c. (ii) Is \stone, n)de(m) de(n) + f \/ s(m, n)dexn) de(m). . if x = y 2. Let (X, A, u) = (Y,B, v) = (N, M,c). Here, N is the set of natural numbers, M= 2N, and c is the counting measure defined by setting c(E) equal to the number of points in E if E is finite and oo if E is an infinite set. Define f: NN R by setting 2 - 2-3 f(x, y) -2 + 2-3 if x = y +1 0 otherwise. Show that (i) f is measurable with respect to the product measure c X c. (ii) Is \stone, n)de(m) de(n) + f \/ s(m, n)dexn) de(m)