Hi !

Here is my problem:

(The questions are independent)

a/

If f is a function integrable on [0,b] and

g(x) =

pour 0xb.

Prove that g is integrable on [0,b] and that

= .

b/

Let f be a fonction that is measurable, finite-valued on [0,1], and such that |f(x)-f(y)| is integrable on [0,1]x[0,1].

Prove that f(x) est intégrable sur [0,1].

For part a/, using Fubini's theorem, I managed to show g is integrable, but cannot get the equality :

= .

For part b/, i set g(x,y) = |f(x)-f(y)|, integrable, and tried to use Fubini's, but don't really see what I can do with:

.

Any ideas ?