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