Since we may apply the geometric series

Now I'll show that: valid

Consider the Riemannian sum:

By the Power Mean inequality we have:

Thus: and:

So we have:

This may also be shown applying Hölder's Inequality

Assuming uniform convergence *

Applying the inequality we've just proved:

Which yields:

This last step is correct since:

By the way, there's equality iff the function is constant.