Definition:Probability Space

From ProofWiki
Jump to navigation Jump to search

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 $\mathcal E$.


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

$\Omega$ is called the sample space of $\mathcal E$
$\Sigma$ is called the event space of $\mathcal E$
$\Pr$ is called the probability measure on $\mathcal E$.


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.


Sources