probability space

概率空间

Probability · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A triple $(\Omega,\mathcal F,P)$ in which $\mathcal F$ is a sigma-algebra on $\Omega$ and $P$ is a countably additive nonnegative measure with $P(\Omega)=1$.

由样本空间、事件的σ代数及总质量为1的概率测度组成的三元组。

Example

For a fair four-sided die, $P(\{1,3\})=1/2$.

Usage and distinctions

A sample space alone does not specify which events are measurable or their probabilities.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Gregory F. Lawler — Notes on ProbabilitySection 1, Probability spaces, opening definition · Checked 2026-10-14

Translation sources

1. 李东风 — 应用随机过程（北京大学）§1.1.4 概率，定义1.5 · Checked 2026-10-14

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.