Further Analysis | Part IB, 2003

(a) State and prove Morera's Theorem.

(b) Let DD be a domain and for each nNn \in \mathbb{N} let fn:DCf_{n}: D \rightarrow \mathbb{C} be an analytic function. Suppose that f:DCf: D \rightarrow \mathbb{C} is another function and that fnff_{n} \rightarrow f uniformly on DD. Prove that ff is analytic.

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