The problem is Excercise 5. in page 88 of Folland's "real analysis: modern techniques and their applications", 2nd edition, as the image below shows.
As the hint indicates, we should use Excercise 4. From Excercise 4, if signed measure , then . Supposing , , we have . Then it follows . But at the same time , , so also . I really have no idea how to employ Excercise 4. to prove . Can you help me? Thanks in advance!