An Infinitesimal Circular Morera Theorem

Qiteng Guo, Ao Xiao

We prove an infinitesimal circular version of Morera's theorem. Let $D\subset \mathbb{C}$ be a domain and let $f\in C(D)$. If, at every $a\in D$, $\int_{\vert{}ζ-a\vert{}=r}f(ζ)\,dζ…