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A note on invariance of the Cauchy and related distributions
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A note on invariance of the Cauchy and related distributions
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math.PR
math.CV
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cauchynoterelatedaboveanalyticcomplexconcernsdistribution
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It is known that if $f$ is an analytic self map of the complex upper half-plane which also maps $\mathbb{R}\cup\{\infty\}$ to itself, and $f(i)=i$, then $f$ preserves the Cauchy distribution. This note concerns three results related to the above fact.
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