Does the identity principle hold for meromorphic functions? (The identity principle states that if $Q$ is a connected set and $f(z)= g(z)$ for all $z$ in some subset $A$ of $Q$ which has limit points in $Q$, then $f(z) = g(z)$ for all $z$ in $Q$)
Does the identity principle hold on meromorphic functions?
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complex-analysis
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1Work with $f - g$. If $f$ and $g$ agree on a set with a limit point, then the limit point is a removable singularity of $f - g$. ("Poles of both functions" should have been "poles of either function" above; I meant for "both" to be applied to "poles" and not to "functions.") Also, you want $Q$ to be open. – 2012-09-02