Definition:Event Space

Definition
Let $\EE$ be an experiment whose probability space is $\struct {\Omega, \Sigma, \Pr}$.

The event space of $\EE$ is usually denoted $\Sigma$ (Greek capital sigma), and is the set of all outcomes of $\EE$ which are interesting.

By definition, $\struct {\Omega, \Sigma}$ is a measurable space.

Hence the event space $\Sigma$ is a sigma-algebra on $\Omega$.

That is:

Also denoted as
Some sources use $\FF$ or $\mathscr F$ to denote an event space.

In the field of decision theory, the symbol $\Xi$ can often be seen.

Also see

 * Elementary Properties of Event Space