Let $T_1, T_2, T_3, \, \ldots \overset{d}{=} \text{Exponential}(1)$ each be a D4000: Standard exponential random positive real number such that

(i)	$T_1, T_2, T_3, \, \ldots$ is an D2713: Independent random collection

A D6135: Random unsigned real process $X : [0, \infty) \to \text{Random}(\Omega \to [0, \infty))$ is a standard real poisson process if and only if \begin{equation} \forall \, t \in [0, \infty) : X_t \overset{d}{=} \max \left\{ N \in \mathbb{N} : \sum_{n = 1}^N T_n \leq t \right\} \end{equation}