Let $D$ be a simply connected domain in $\C$.
Let $f: D \to \C$ be a continuous function.
Let $f$ be such that:
- $\displaystyle \int_\gamma \map f z \rd z = 0$
Then $f$ is analytic on $D$.
For a fixed $z_0 \in D$ and $z \in D$ we consider the function:
- $\displaystyle \map F z = \int_\gamma \map f w \rd w$
where $\gamma$ is any (simple) contour starting at $z_0$ and ending at $z$.
This is the converse of the Cauchy-Goursat Theorem.
Source of Name
This entry was named for Giacinto Morera.