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Probability space

by , PhD

A probability space is a triple [eq1], where Omega is a sample space, $\tciFourier $ is a sigma-algebra of events and $QTR{rm}{P}$ is a probability measure on $\tciFourier $.

Table of Contents

Elements of a probability space

The three building blocks of a probability space can be described as follows:


Suppose the probabilistic experiment consists in extracting a ball from an urn containing two balls, one red ($R$) and one blue ($B$).

The sample space is[eq2]

A possible sigma-algebra of events is[eq3]where the event $emptyset $ (the empty set) could be described as "nothing happens", the event Omega could be described as "either a blue ball or a red ball is extracted", the event $\left\{ R\right\} $ could be described as "a red ball is extracted", and the event $\left\{ B\right\} $ could be described as "a blue ball is extracted".

A possible probability measure $QTR{rm}{P}$ on $\tciFourier $ is[eq4]

More details

The lecture entitled Probability contains a more detailed explanation of the concept of probability space and of the properties that must be satisfied by its building blocks.

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