\begin{definition}[Definition:Limit of Sequence of Events/Increasing]
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $\sequence {A_n}_{n \mathop \in \N}$ be an increasing sequence of events.
Then the union:
:$\ds A = \bigcup_{i \mathop \in \N} A_i$
of such a sequence is called the '''limit of the sequence $\sequence {A_n}_{n \mathop \in \N}$'''.
From the definition of event space we have that such a $\ds \bigcup_{i \mathop \in \N} A_i$ is itself an event.
\end{definition}