Definition:Probability Space

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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 $\Pr$.


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