5.

(a) Verify that the hypotheses of Fubini's Theorem hold when f is continuous on R.

(b) Modify the proof of Remark 12.33 to show that Fubini's Theorem might not hold for a nonintegrable

f, even if f(x, y) is continuous in each variable separately;

i.e., if f(x,·) is continuous for each x E [a, b] and f(·, y) is continuous for each y E [c, dj.