| Version 5 |
Version 4 |
| If the functions $f$ and $g$ are holomorphic in a domain $\mathbf{D}$ of |
If the functions $f$ and $g$ are holomorphic in a domain $\mathbf{D}$ of |
| the complex plane and the equation |
the complex plane and the equation |
| \begin{align} |
\begin{align} |
| f(z) = g(z) |
f(z) = g(z) |
| \end{align} |
\end{align} |
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is true in an infinite subset $S$ of $\mathbf{D}$ having an accumulation point $z_0$ in $\mathbf{D}$, then (1) is true in the whole $\mathbf{D}$.
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is true in an infinite subset $S$ of $\mathbf{D}$ having an accumulation point $z_0$ in $A$, then (1) is true in the whole $A$.
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| \textbf{Remark.}\, The subset $S$ may be e.g. some neighbourhood of $z_0$ or some arc containing $z_0$. |
\textbf{Remark.}\, The subset $S$ may be e.g. some neighbourhood of $z_0$ or some arc containing $z_0$. |
