identity theorem of holomorphic functions

If the functions $f$ and $g$ are holomorphic in a domain $D$ ofthe complex plane and the equation

\\displaystyle f(z)=g(z)

(1)

is true in an infinite subset $S$ of $D$ having an accumulation point $z_{0}$ in $D$ , then (1) is true in the whole $D$ .

Remark. The subset $S$ may be e.g. some neighbourhood of $z_{0}$ or some arc containing $z_{0}$ .

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