In this paper we construct a Cauchy integral for the distributions in 𝒮′, the tempered distributions, and obtain various properties concerning this Cauchy integral. Our main goal is to show that the ...

A real random variable $X$ has a Cauchy law $C(a, b)$ if its density is $b\pi^{-1}\lbrack (x - a)^2 + b^2 \rbrack^{-1}$, with $b > 0$ and $a$ real. Let $f$ be a ...