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
Event
Definition D5500
Almost sure event
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space.
An D1716: Event $E \in \mathcal{F}$ in $P$ is an almost sure event in $P$ if and only if \begin{equation} \mathbb{P}(E) = 1 \end{equation}
Results
R4331: Probability of binary intersection with an almost sure event
R4326: Probability of binary union with almost sure event
R4329: Probability of countable intersection with an almost sure event
R4327: Probability of countable union with an almost sure event
R4330: Probability of finite intersection with an almost sure event
R4328: Probability of finite union with an almost sure event