Morera's Theorem states that if a function is continuous on a region and the integral of that function over every closed curve in that region is zero, then the function is analytic (holomorphic) within that region. This theorem connects the concepts of differentiability and analyticity, emphasizing how certain conditions on integrals can determine the behavior of functions in complex analysis. It serves as a powerful tool in proving a function's analyticity without needing to explicitly show that the function is differentiable at every point.
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