Integrals over circles passing through the origin and a characterization of analytic functions (Q1122680)

The author shows that if f is a continuous function in the unit disk \(\Delta\) such that for some \(\epsilon >0\), \(\int_{\Gamma}f(z)dz=0\) for every circle \(\Gamma\) \(\subseteq \Delta\) such that \(\Gamma\) \(\cap \{z:\) \(| z| <\epsilon \}\neq \emptyset\), then f is holomorphic in \(\Delta\).