Folland Chapter 3 Exercise 17

Solution to exercise 3.17 from Gerald Folland's textbook, "Real Analysis: Modern Techniques and Their Applications."

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[LuisFlores-mujc]

I think you have to do the case where f is non-negative first, and then do the general case where f = f+ - f-. Otherwise, your measures lambda and rho are signed measures and you have to be careful when saying that they are finite.