Probability of Limit of Sequence of Events/Decreasing

Theorem
Let $\left({\Omega, \Sigma, \Pr}\right)$ be a probability space. Let $\left \langle{B_n}\right \rangle_{n \mathop \in \N}$ be a decreasing sequence of events.

Let $\displaystyle B = \bigcap_{i \mathop \in \N} B_i$ be the limit of $\left \langle{B_n}\right \rangle_{n \mathop \in \N}$.

Then:
 * $\displaystyle \Pr \left({B}\right) = \lim_{n \to \infty} \Pr \left({B_n}\right)$

Proof
Set $A_i = \Omega \setminus B_i$ and then apply De Morgan's laws and the result for an increasing sequence of events.