Standard Cauchy random real number

▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Collection of sets
▾ Set union
▾ Successor set
▾ Inductive set
▾ Set of inductive sets
▾ Set of natural numbers
▾ Set of integers
▾ Set of rademacher integers
▾ Rademacher integer
▾ Rademacher random integer
▾ Standard rademacher random integer
▾ Standard gaussian random real number
▾ Gaussian random real number
▾ Student's random real number

Standard Cauchy random real number

Formulation 0

Let $X \in \text{Student}(1)$ be a D4861: Student's random real number.
A D3161: Random real number $C \in \text{Random}(\mathbb{R})$ is a standard Cauchy random real number if and only if \begin{equation} C \overset{d}{=} X \end{equation}