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 $\Pr$.

Also see

 * Definition:Probability Measure
 * Definition:Probability Function