Please show that :
if and
then
thanks very much
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.