Well, it isn't in general! If you forgot to include the hypotheses that f and g are themselves integrable, then you can use the fact that |f- g|= f- g as long as f(x)> g(x) and |f- g|= g- f as long as f(x)< g(x).

Nov 11th 2008, 11:29 AM

ThePerfectHacker

Quote:

Originally Posted by Coda202

Show that:

|f - g| is integrable.

If are integrable then are integrable.
And if is integrable then is integrable.

Therefore, if are integrable then is integrable and that implies is integrable.