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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Poisson kernel is the Cauchy distribution, reference?

Let $d = 2$, and consider the domain $D = \mathbb{H}$, the upper half-plane. Can someone give me a reference to a proof that the Poisson kernel is the Cauchy distribution?
Roger Smyth's user avatar