ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation 0
Let $\xi = \{ \{ \xi_{n, m} \}_{1 \leq m \leq n} \}_{n \geq 1}$ be a D5164: Random real standard triangular array such that
(i) \begin{equation} \forall \, n \in 1, 2, 3, \ldots : \forall \, m \in 1, \ldots, n : \xi_{n, m} \overset{d}{=} \text{Bernoulli}(1 / n) \end{equation}
(ii) $\xi_{n, 1}, \ldots, \xi_{n, n}$ is an D2713: Independent random collection for each $n \geq 1$
A D5216: Random natural number $X \in \text{Random}(\mathbb{N})$ is a standard Poisson random natural number if and only if \begin{equation} X \overset{d}{=} \lim_{n \to \infty} \sum_{m = 1}^n \xi_{n, m} \end{equation}