Definition. Let $\Omega$ be a finite or countable set. Let $p:\Omega\rightarrow[0,1]$ be a function such that \[\sum_{\omega\in\Omega}p_{\omega}=1.\]

Then $(\Omega,p)$ is called a discrete probability space. $\Omega$ is called the sample space and $p_{\omega}$ are called elementary probabilities.

定义: 设 $\Omega$ 是一个有限集或可数集. 设 $p:\Omega\rightarrow[0,1]$ 是 $\Omega$ 上的一个函数, 满足 \[\sum_{\omega\in\Omega}p_{\omega}=1.\]

则 $(\Omega,p)$ 被称为一个离散概率空间. $\Omega$ 被称为样本空间, $p_{\omega}$ 称作为基本概率.

References:

Manjunath Krishnapur, Probability and Statistics