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, 12:29 PM
Originally Posted by Coda202
|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.