I'm stuck trying to prove a step inside a lemma from Serre; given is
I've tried using Cauchy-Schwartz for integrals, but this step is too big (using Mathematica, it lead to a contradiction); something simpler must do the trick.
Thanks in advance.
What Moo says is correct (as always). If f is a (complex-valued) function of a real variable t on the interval [a,b], let be a Riemann sum for f (where P is the partition given by the points and each is a point in ). Then the triangle inequality shows that . In the limit, as the mesh of the partition goes to 0, it follows that .