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If $f:D\to D’$ is analytic and $u: D'\to R$ is harmonic then the composition of $u$ and $f$ is harmonic in $D$.

How can I show that the above statement is true/false? Can anyone help me?

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    This question was already discussed [here](http://math.stackexchange.com/questions/151827/composition-of-a-harmonic-function)... – 2012-11-23

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Locally every harmonic function $u$ is the real part of an analytic function $g$, so locally $u \circ f = \operatorname{Re} (g \circ f)$ is the real part of an analytic function, hence harmonic. A function which is everywhere locally harmonic is globally harmonic, showing that the statement is true.