10.6.16 Analytic functions

Problem: Let function \( f_{1}(z), f_{2}(z) \) are analytic in a domain \( D \subset \mathbb{C} \) of the complex plane, and they coincide at \( E \subset \) \( D\left(f_{1}(z) \equiv f_{2}(z), \forall z \in E\right) \) and let \( E \) have at least one limit point in \( D \), then \( f_{1}(z) \equiv f_{2}(z), \forall z \in D \).