\begin{definition}[Definition:Eventually (Probability Theory)]
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $\sequence {E_n}_{n \mathop \in \N}$ be a sequence of events in $\Sigma$. 
We define: 
{{begin-eqn}}
{{eqn	| l = \set {E_n \text { eventually} }
		| r = \set {\omega \in \Omega : \text {there exists } N \in \N \text { such that } \omega \in E_n \text { for } n \ge N}
}}
{{eqn	| r = \liminf_{n \mathop \to \infty} E_n
}}
{{end-eqn}}
where $\ds \liminf_{n \mathop \to \infty} E_n$ is the limit inferior of $\sequence {E_n}_{n \mathop \in \N}$.
\end{definition}