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 a null event
Probability of complement of an almost sure event
Probability of set difference
Probability of union with the impossible event