Definition:Probability Space

Definition

A probability space is a measure space $\struct {\Omega, \Sigma, \Pr}$ in which $\map \Pr \Omega = 1$.

A probability space is used to define the parameters determining the outcome of an experiment $\EE$.

In this context, the elements of a probability space are generally referred to as follows:

$\Omega$ is called the sample space of $\EE$

$\Sigma$ is called the event space of $\EE$

$\Pr$ is called the probability measure on $\EE$.

Thus it is a measurable space $\struct {\Omega, \Sigma}$ with a probability measure $\Pr$.

Then $\left({\Omega, \Sigma, \Pr}\right)$ is known as a discrete probability space.

Let $\Omega$ be a continuum.

Then $\left({\Omega, \Sigma, \Pr}\right)$ is known as a continuous probability space.