\begin{definition}[Definition:Increasing Sequence of Events]
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $\sequence {A_n}$ be a sequence of events in $\Sigma$.
Then $\sequence {A_n}$ is described as '''increasing''' {{iff}}:
:$\forall i \in \N: A_i \subseteq A_{i + 1}$
\end{definition}