Definition:Probability Space

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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.


Sources