ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Subset structure
Measurable space
Measure space
Probability space
Single boolean trial probability space
Definition D5511
Standard single boolean trial probability space
Formulation 0
A D5107: Triple $P = (\Omega, \mathcal{F}, \mathbb{P})$ is the standard single boolean trial probability space if and only if
(i) \begin{equation} \Omega = \{ 0, 1 \} \end{equation}
(ii) \begin{equation} \mathcal{F} = \{ \emptyset, \{ 0 \}, \{ 1 \}, \{ 0, 1 \} \} \end{equation}
(iii) \begin{equation} \mathbb{P} \{ 0 \} = \mathbb{P} \{ 1 \} = \frac{1}{2} \end{equation}