**probability space**if and only if

(1) | $M = (X, \mathcal{F})$ is a D1108: Measurable space |

(2) | $\mu$ is a D198: Probability measure on $M$ |

▾ 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

▾ 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

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

» D1720: Independent event collection

» D1673: Sample space

» D6122: Standard uniform discrete probability space

Results