# sampling using L1 optimization

As much as I understand the F should be the interval medians (correct me if I wrong), according to the next slide, where is also the Loss function defined:

What I don't understand is the next note in the question:

What does this assumption gives me ? Why do I need it ? What information does it gives me that the integral over the reciprocal of $$f$$ is 0 ? How does this assumption expressed in the proof of the MAD or in it's loss? Thank you in advance.