▾ 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
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 $M$
Also known as
Stochastic space, Probability calculus
Child definitions
» D1716: Event
» D1720: Independent event collection
» D1673: Sample space
» D6122: Standard uniform discrete probability space
Results
» R1338: Probabilistic Borel-Cantelli lemma
» R2060: Probability of set difference
» R3646: Countable partition additivity of probability measure
» R3719: Probability of complement event
» R4073: Probability of union with the impossible event
» R4278: Expression for probability of event in terms of complement event
» R4559: Probability of complement of an almost sure event
» R4560: Probability of complement of a null event
» R4928: Finite partition additivity of probability measure
» R4929: Binary partition additivity of probability measure
» R5318: Unions need not preserve equality in probabilities for events
» R5317: Intersections need not preserve equality in probabilities for events