Let be a sequence of functions which are defined on , and uniformly converges there to bounded function . Let which is continuous function on all .
Prove that the sequence uniformly converges and find the limit function.
Thank you!
Let be a sequence of functions which are defined on , and uniformly converges there to bounded function . Let which is continuous function on all .
Prove that the sequence uniformly converges and find the limit function.
Thank you!
What have you tried? Are you going to just use the definition? If so, maybe seeing what is equal to would help. First, just as a matter of formality we really are considering where and the restriction of a continuous function is continuous. So, let . Then, for a fixed we have that so that we see . Now, tell me, what did I use at ?