Let $G_1 \in \text{Gamma}(\alpha_1, 1), \; \ldots, \; G_N \in \text{Gamma}(\alpha_N, 1)$ each be a D3838: Gamma random positive real number such that

(i)	$G_1, \ldots, G_N$ is an D2713: Independent random collection

A D4383: Random euclidean real number $X \in \text{Random}((0, 1)^N)$ is a Dirichlet random euclidean real number with parameter $\alpha = (\alpha_1, \ldots, \alpha_N)$ if and only if \begin{equation} X \overset{d}{=} \frac{1}{\sum_{n = 1}^N G_n} (G_1, \ldots, G_N) \end{equation}