Question
Let $\left(A_{n}\right)_{n \geq 1}$ be any sequence of pairwise disjoint events and $P$ a probability. Show that $\lim _{n \rightarrow \infty} P\left(A_{n}\right)=0$.
Step 1
Since the events $A_n$ are pairwise disjoint, this means that for any $n \neq m$, we have $A_n \cap A_m = \emptyset$. In other words, no two events in the sequence can occur simultaneously. Show more…
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