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
Definition D1159
Probability space
Formulation 0
A D5107: Triple $M = (X, \mathcal{F}, \mu)$ is a probability space if and only if
(1) $M = (X, \mathcal{F})$ is a D1108: Measurable space
(2) $\mu$ is a D198: Probability measure on $M$
Children
▶ Event
▶ Independent event collection
▶ Sample space
▶ Standard uniform discrete probability space
Results
▶ Binary partition additivity of probability measure
▶ Countable partition additivity of probability measure
▶ Expression for probability of event in terms of complement event
▶ Finite partition additivity of probability measure
▶ Probabilistic Borel-Cantelli lemma
▶ Probability of complement event
▶ Probability of complement of an almost sure event
▶ Probability of complement of a null event
▶ Probability of set difference
▶ Probability of union with the impossible event