Main Question or Discussion Point
In my Complex Analysis text, Morera's theorem states that a continious function whose domain is a region G is analytic if [tex]\int_T f=0[/tex] for every triangular path T in G. However, other versions of the theorem state that the integral must be zero for any simple closed curve in G. Can someone explain how one can go from the first statement to the second one? It doesn't have to be a full proof; just a heuristic argument. I'm just curious. It's probably something to do with the fact that any curve can be segmented into straight line segments or something, but I haven't taken any topology courses so I don't even really know what I'm taking about.