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

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- November 30th 2008, 12:10 PMakolmanConvergence of a sequence of functions
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 - November 30th 2008, 10:23 PMakolman
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? - November 30th 2008, 11:21 PMCaptainBlack
- November 30th 2008, 11:54 PMakolman
- December 1st 2008, 02:09 AMCaptainBlack
- December 1st 2008, 02:18 AMakolman
I get the difference now, so how do you do this proof?

Thanks in advance. - December 2nd 2008, 11:56 AMakolman
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.