Cauchy's Integral Theorem says that if a function is analytic in open and simply connected domain and $\gamma$ is a closed curve so:
$$\int_\gamma f(z) \, dz=0$$
Morera Theorem says that if a function is continuous on an open domain such that for every closed curve $$\int_\gamma f(z) \, dz=0$$ So: the function is analytic
So those both theorem are two different directions of iff statement?
Best Answer
Morera Theorem is usually considered a converse of the Cauchy integral theorem but it is not (usually) presented as an iff statement because the two theorems can be formulated with some differences on the conditions.
Using the same conditions we can say that, if $f$ is a continuous function on simply-connected region $D$, the the Cauchy theorem says:
$f$ is analytic $\Rightarrow$ $f$ has an antiderivative
and the Morera's theorem says
$f$ has an antiderivative $\Rightarrow$ $f$ is analytic