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I want to prove this geometrically.

For function $g : \mathbf{C} \rightarrow \mathbf{R}$ and g is some continuous function.

The value of $\int_0^{2\pi} g(re^{i(\theta + \phi)}) \, d\phi$ is independent of $\theta$?

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    You go around the whole circle once. It doesn't matter at which point on the circle you start. The parameter $\theta$ only identifies the starting point.2012-06-12
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    What would be a geometric proof of this? That the measure is translation invariant?2012-06-12

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