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Theorem: If a function f is analytis throughout a simply connected domain D, then for every closed contour C lying in D, the integral is o along the contour.

This is a theorem from the text I am using without complete proof. The problem is that when the closed contour has an infinite number of self-intersection points. Who can give me a rigorous proof or a reference about it?

Thanks

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    Rudin's _Real and Complex Analysis_ gives a rigorous argument that does not break down under infinite self-intersection.2010-12-01
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    @Akhil Mathew: On what page?2010-12-01
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    It's somewhere in the chapter on elementary properties of holomorphic functions (#10).2010-12-01

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You can find a proof in Section IV.6 of J.B. Conway's Functions of one complex variable.