ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
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▼ 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 $M$
Also known as
Stochastic space, Probability calculus
Children
▶ D1716: Event
▶ D1720: Independent event collection
▶ D1673: Sample space
▶ D6122: Standard uniform discrete probability space
Results
▶ R4929: Binary partition additivity of probability measure
▶ R3646: Countable partition additivity of probability measure
▶ R4278: Expression for probability of event in terms of complement event
▶ R4928: Finite partition additivity of probability measure
▶ R5711: Inclusion-exclusion principle for probability of binary union for disjoint sets
▶ R1338: Probabilistic Borel-Cantelli lemma
▶ R3719: Probability of complement event
▶ R4560: Probability of complement of a null event
▶ R4559: Probability of complement of an almost sure event
▶ R2060: Probability of set difference
▶ R4073: Probability of union with the impossible event