I am pretty confused, does pointwise convergence means
???
Also, I noticed that if the all are continuous, then the proof wouldn't be hard. However, they are not mentioning anything, is continuity necessary? How can I prove that?
Suppose is a sequence of functions converging uniformly to . Define . Show that the sequence converges pointwise to f.
So I need to show that
Thanks in advance
If I let , then . I know that converges uniformly to
such that for
Since converges uniformly to ,
such that for ,
Is this right?
If I let ,
I am sorry if I pushing this question too much, but I am still clueless.