# Definition:Probability Space

## Definition

A probability space is a measure space $\left({\Omega, \Sigma, \Pr}\right)$ in which $\Pr \left({\Omega}\right) = 1$.

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

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

### Discrete Probability Space

Let $\Omega$ be a discrete sample space.

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

### Continuous Probability Space

Let $\Omega$ be a continuum.

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

## Also see

• Results about probability theory can be found here.