A D5107: Triple $P = (\Omega, \mathcal{F}, \mathbb{P})$ is a standard uniform discrete probability space with respect to $N \in \{ 1, 2, 3, \ldots \}$ if and only if

(1)	$$\begin{equation} \Omega = \{ 1, 2, \ldots, N \} \end{equation}$$
(2)	$$\begin{equation} \mathcal{F} = \mathcal{P}(\Omega) \end{equation}$$
(3)	$$\begin{equation} \forall \, n \in \{ 1, 2, \ldots, N \} : \mathbb{P} \{ n \} = \frac{1}{N} \end{equation}$$