Lecture 29: Necessary & Sufficient Conditions for Convergence
Now, using the above lemma with and , where . It follows that
(8.24)
where
(8.25)
Since is uniformly continuous on . In view of this fact and of (8.21) the above bound for tends to zero as for every , establishing the proof of the theorem.
and 
, where 
. It follows that 
is uniformly continuous on 
. In view of this fact and of (8.21) the above bound for 
tends to zero as 
for every 
, establishing the proof of the theorem. 
