\begin{definition}[Definition:Event Space]
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:
{{begin-axiom}}
{{axiom | n = \text {ES} 1
        | lc= Non-Empty:
        | ml= \Sigma
        | mo= \ne
        | mr= \O
}}
{{axiom | n = \text {ES} 2
        | lc= Closure under Set Complement:
        | q = \forall A \in \Sigma
        | ml= \Omega \setminus A
        | mo= \in
        | mr= \Sigma
}}
{{axiom | n = \text {ES} 3
        | lc= Closure under Countable Unions:
        | q = \forall A_1, A_2, \ldots \in \Sigma
        | ml= \bigcup_{i \mathop = 1}^\infty A_i
        | mo= \in
        | mr= \Sigma
}}
{{end-axiom}}
\end{definition}