Hi again !

This time, I'm really struggling with a problem...

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Let be the set of functions defined over , continuous, with real values.

. Let F be the antiderivative of f that annulates in 0.

Let E be the subset of functions f in such that converges.

Previous questions...

1/ Determine the positive functions f in E such that .

It's ok, f=0.

2/ Let f be apositivefunction of

Show :

It's ok for this.

Problem :

Find an example for f (necessarily not of constant sign) in E and such that diverges.

Thanks for your help, we are really struggling with that

(and I have no assignment, I'm asking several questions these days because I have an exam tomorrow )