Definition: Probability space
Index:
The Book of Statistical Proofs ▷
General Theorems ▷
Probability theory ▷
Random experiments ▷
Probability space
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Metadata: ID: D167  shortcut: probspc  author: JoramSoch  date: 20211126, 14:30.
Definition: Given a random experiment, a probability space $(\Omega, \mathcal{E}, P)$ is a triple consisting of

the sample space $\Omega$, i.e. the set of all possible outcomes from this experiment;

an event space $\mathcal{E} \subseteq 2^\Omega$, i.e. a set of subsets from the sample space, called events;

a probability measure $P: \; \mathcal{E} \rightarrow [0,1]$, i.e. a function mapping from the event space to the real numbers, observing the axioms of probability.
 Wikipedia (2021): "Probability space"; in: Wikipedia, the free encyclopedia, retrieved on 20211126; URL: https://en.wikipedia.org/wiki/Probability_space#Definition.
Metadata: ID: D167  shortcut: probspc  author: JoramSoch  date: 20211126, 14:30.