# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 154: Morera’s Theorem

In complex analysis, Morera’s Theorem states that if $D \subset \mathbb{C}$ is a region (open, path-connected) and $f: D \rightarrow \mathbb{C}$ is continuous and has the property that

$\int _\gamma f(z) dz = 0$

for any closed curve $\gamma \subset D$, then $f$ is holomorphic.

This is an immediate corollary to the observation in [153], since if $F$ is a primitive of $f$ on $D$ then $f$ itself is holomorphic on $D$.