Another practice exam exercise:

I can't do part (a) at all, and I'm not much further along on part (b). If I use the result of (a), all I need is to show that , and then part (b) follows from Weierstrass. But I cannot show that , nor can I show part (a) at all.Suppose is an analytic function in for which is finite.

(a)Prove for that .

(b)If is a sequence of analytic functions in for which

for , and

as , prove converges to uniformly on compact subsets of .

I also notice that is not explicitly defined. I presume it's just some arbitrary (but fixed) subset of . But perhaps it's a misprint...? I don't know...

As usual, any help would be appreciated!