Probability of Limit of Sequence of Events/Decreasing

Theorem
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space. Let $\sequence {B_n}_{n \mathop \in \N}$ be a decreasing sequence of events.

Let $\ds B = \bigcap_{i \mathop \in \N} B_i$ be the limit of $\sequence {B_n}_{n \mathop \in \N}$.

Then:
 * $\ds \map \Pr B = \lim_{n \mathop \to \infty} \map \Pr {B_n}$

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