▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
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▾ Power set
▾ Hyperpower set sequence
▾ Hyperpower set
▾ Hypersubset
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▾ Measure space
▾ Probability space
Standard uniform discrete probability space
Formulation 0
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}