Morera's theorem states that a function continuous on a domain is analytic if the contour integral over every axis-aligned rectangle contained in the domain vanishes; it provides a converse-style route to establishing analyticity from continuity plus a vanishing-integral condition, rather than from the definition of complex differentiability directly. It belongs to complex analysis, sitting within the theory of complex integration alongside Cauchy's theorem and the Cauchy integral formula, and its corollaries extend analyticity-preservation results to functions defined by parametrized integrals and to functions that are analytic apart from a line where only continuity is known.
Morera's theorem states that a function continuous on a domain is analytic if the contour integral over every axis-aligned rectangle contained in the domain vanishes; it provides a converse-style rou…